Why does the Left object to these rules by the Republicans when it comes to voting?

It's simply a matter of perceived advantage...on both sides of the issue.

The (shared) perception is this:

- of the people prevented from voting by strict voter identification and authentication regulations

- more of those people would vote Democrat than would vote Republican

Thus - naturally -

- Republicans want strict voter identification and authentication regulations

- Democrats want less strict voter identification and authentication regulations

From what I consider an objective standpoint

- myself, member of no political party

--- naturally we don't want votes from people whom the Constitution and Federal Law does not allow to vote

--- therefore, naturally we should have strict regulations in place to ensure that such voting does not take place - i.e. to defend against illegal and fraudulent voting

--- naturally any and all such identification and authentication regulations should make it possible - without undue difficulty, including poverty-related issues - for all legal voters to acquire necessary identification and authentication to vote

--- on the other hand, a person who makes no attempt to acquire such identification or authentication should not be rewarded for their laziness by being granted permission to vote. Why: because the lack of such identification and authentication is what enables illegal and fraudulent voting, which thing DESPERATELY NEEDS to be prevented.

In other words:

- You want to vote?

- Then get a valid state ID, with strict identification and authentication measures in place.

- You can't afford such an ID?

- Then the state should pay for it.

- You don't have transportation to a state ID distribution center?

- Then the state should be willing to supply transportation at their expense.

Because that's not what Republicans are concerned about and not what many of these laws are aimed at. 

Republicans, by which I mean Republican politicians and political operatives, are concerned that they can't win free and fair elections anymore.  The mania for these types of laws really began after Barack Obama won the Presidency in 2008.  Republicans were horrified, especially by Obama's expansion of the Democratic map into areas like Virginia and North Carolina.  Other elections saw Democrats winning often narrow victories in states which they had previously not been competitive in.  Republicans realized that the American people rejected their candidates and ideas too often.  So they've set out to "fix" this problem by trying to whittle down the electorate to make it more favorable to Republicans.  They've done this through various laws aimed at making it more difficult for people to vote.  The logic here is that Republican voters are often considered more motivated than Democrats, meaning that obstacles to voting will disproportionately impact Democrats.  They've also in many cases tailored these laws to try and make them impact Democrats rather than Republicans.  For example, in Texas the voter ID law will not accept a student ID, even from a state run school.  This is because younger people, especially college students, are believed to vote more Democratic.  But the law does accept a concealed carry permit as valid for voter ID purposes, under the logic that people interested in carry concealed weapons are more likely to be conservative.  When North Carolina drafted its voter ID law, the Republicans in the legislature actually sought out information on what types of ID (other than drivers licenses of course) were most popular among African Americans and excluded many of those from qualifying.  In Pennsylvania, the Republican leader of the legislature which passed a voter ID law admitted in 2012 that they passed it "In order to make sure that Mitt Romney wins Pennsylvania). 

We also know that these laws have little to do with fraud because many of the provisions wouldn't impact fraudulent voting at all.  For example, Georgie just passed a law which makes it illegal for people to hand out food or water to someone waiting in line to vote.  This has no impact on fraud, but does make the experience of waiting in line less pleasant, perhaps causing people to decide to not vote.  In North Dakota, the Republicans passed a voter ID law which required that driver's licenses and other IDs used to satisfy the law have a street address on it.  This has nothing to do with fraud, since one can prove ones identity with the ID anyway.   Instead it was aimed at disfranchising  Native American voters, many of whom lack street addresses because they live in rural areas without home delivery, because their votes were critical to electing Democratic Senator Heidi Heitkamp in 2012.  In another state, I forget which one, they passed a law which said that if a person showed up to the wrong polling place, the poll workers could not tell them the right place to go to.  Again, this has nothing to do with fraud, but it does work to disfranchise infrequent voters who may not be well informed about where they should go to vote.  These kinds of laws also work alongside other matters which the GOP have engaged in to limit the ability of the people to choose Democratic politicians.  For example, many states controlled by Republicans have engaged in aggressive gerrymandering to maximize the number of seats they get in elections.  In North Carolina, Democrats and Republicans both got a little over 49% of the vote in House elections in 2020, but Republican gerrymandering meant that they got 8 seats, as opposed to only 5 for Democrats.  Numerous states are gerrymandered like this, and when done on a national level it makes for a real advantage for Republicans.  In Wisconsin, the state legislature is so gerrymandered that a mathematician determined that Democrats would have to get over 60% of the vote to win just 50% of the seats.  So Wisconsin has effectively stopped being a democracy at the state legislative level.  Republicans have also tried to limit voting in ways unrelated to fraud.  For example, in 2018, voters in Florida passed a ballot measure which would have restored voting rights to almost all non violent felons.  But the Republicans who controlled the legislature worked to weaken enforcement of the law and keep people from voting.  This has nothing to do with fraud, but does have to do with Republican fears of more black and Hispanic people, who make up the majority of the ex-con population, voting for Democrats.  Then we have efforts by Republicans to make elections matter less.  In North Carolina and Wisconsin, Gubernatorial victories by Democratic candidates were followed by efforts by the Republican legislatures to strip the Governor's office of powers which they had previously had. 

The conclusion here is inescapable: the problem that Republicans have is not with fraud, as such.  The problem they have is that Democrats keep winning elections. Unable or unwilling to change their rhetoric and policies to appeal to a wider swath of voters, Republicans have instead tried to rig the system so that they can win elections without getting majority approval.

Bull. Following the most closely-scrutinized election in American history, with a massive turnout, Republicans want to make it harder to vote when you life in an urban Democratic district. The only way they can get elected is by cutting the number of voters that way. 

Yap about intended results all you want; actual results are the proof of the pudding. 

GOP leaders say we need restore the public's faith in elections.  The only reason people think that fraud occurred in 2020 election is because Trump said there was fraud.  Not one election official, Democrat or Republican, from any state, identified ANY relevant fraud or cheating.  

But Trump has convinced millions of people that he really won the election.  Of all the lies he told, this was the worst.  Because his flimsy little ego could not accept the loss, he caused millions of the members of his cult to believe he actually won.The GOP Arizona legislature is actually trying to pass a law that allows them to reject the result of an election that they don't like.  Trump tried to destroy American democracy by mob violence.  The American people stopped him from becoming "president" for life.

The people who try to cancel elections over imaginary voter fraud are not interested in fair elections.

There is literally nothing too stupid for you to get behind.

Liberal here....What I object is the removal of voting machines by Republican state officials from black districts to intentionally cause 8 hour plus lines on Election Day. There is no excuse for it, no other reason for this other then an attempt to suppress the vote and republicans have done this in multiple States

Hell, that’s the entirety behind the clause in Georgia’s new legislation that makes it illegal to give food and water to voters standing in line. Because they’re planning on causing long lines, hoping people will leave the line and give up on voting

That is the stated objective, but the reality is that Republicans are trying to force out likely-Democrat voters by enacting harsh restrictions in response to a problem that does not exist. Of course, you can't just come out and publicly say "We want fewer Democrats to vote!" (although we are getting closer to that point it appears), so you have to thinly veil these suppression attempts behind the facade of a legitimate reason. And what better way to do that than to baselessly claim rampant voter fraud?