Here is one lawyer's take on what you are seeing out of the appellate courts in regards to ballet counting.* I think you will find this even-handed, but feel free to critique or set me straight on what the law says. (For the full argument you need to read the full post.)
As far as I can tell, the courts are consistently requiring states to follow state statute, (passed by both houses of a state's congress, and signed by the governor) and are not allowing state administrators or anyone else to make one-time changes based on Covid-19 or any other reason. That seems fair on its face.
They have also previously indicated that they are looking to enforce the status quo, and not allow last minute changes, which they have previously done in prior court cases as well. One can reasonably object that the court's intervention at the last minute is itself a late intervention, and I think that criticism has traction, but they would say they are putting the ball back on the line of scrimmage, after it was moved without permission.
These observations may also explain why we are likely to see different rules in different states. The courts are generally holding each state accountable to their own state statutes, and those statutes vary by state. This may result in a requirement that ballots be received by election day in one state, but merely postmarked by election day in another state.
Rather than looking at these rulings as benefiting Republicans or Democrats, or being handed down by judges appointed by Republicans or Democrats, (though it is hard not to notice the consistency of the prejudice by judges on both sides) we should look at the what state statutes, state constitutions, and the Constitution of the United States say.
On their face, most of the court's rulings appear to be largely fair, and simply an enforcement of each state's neutral election laws.
Here is why they are wrong.
In the context of a global pandemic, strictly enforcing state laws infringes on the right to vote. (The same could be true in the future, due to some other outside disruption, like a terrorist attack on the day of the election, especially one targeted at polling sites.)
This right was most clearly articulated by Chief Justice Earl Warren in Reynolds v. Sims 377 U.S. 533, 555 (1964), when he said, “The right to vote freely for the candidate of one’s choice is of the essence of a democratic society, and any restrictions on that right strike at the heart of representative government. [...] Undoubtedly, the right of suffrage is a fundamental matter in a free and democratic society."
The state statutes do this, without intent, because they fail to protect all citizen's right to vote in the context of a pandemic.
In addition, the impact of Covid-19 has a disproportionate impact on protected groups. Therefore in application, the law unintentionally violates these citizens right to vote in particular. This violates the equal protection clause of the 14th Amendment.
While the right to vote was not originally granted to citizens by the U.S. Constitution, the 26th Amendment extended the obvious, but as yet unwritten right to vote to all people over the age of 18. (Unwritten in the US Constitution.)
It would be a strange thing indeed then to say that the Constitution does not grant a right, which the 26th amendment grants to all adults, by prohibiting discrimination on the basis of age.
In fact, four of the fifteen post-Civil War constitutional amendments were ratified to extend voting rights to different groups of citizens. These extensions state that voting rights cannot be denied or abridged based on the following:
"Race, color, or previous condition of servitude" (Fifteenth Amendment, 1870)
"On account of sex" (Nineteenth Amendment, 1920)
"By reason of failure to pay any poll tax or other tax" for federal elections (Twenty-fourth Amendment, 1964)
"Who are eighteen years of age or older, to vote, shall not be denied or abridged by the United States or by any state on account of age" (Twenty-sixth Amendment, 1971)
(Hat-tip to Wikipedia for that last little bit)
Note that those who regularly make use of arguments based on what the text says, or what its original meaning was, rarely want to take a close look at the original intent of the various amendments. (Conservatives are especially allergic to the 14th Amendment's equal protection clause.) In the next few days you are likely to hear some talking heads state that the Constitution does not give anyone the right to vote. It does.
State law as recently applied by the courts, violates the equal protection clause of the Constitution, because even though they are written and intended to be neutral laws, as applied in our current context, the laws have a disproportionate impact on a number of protected groups, including women and people of color.
In other legal contexts, we have precedence for how to deal with instances where a law that was intended to be neutral, nonetheless has a disproportionate impact on one group or another. Some of these examples have to do with religious freedom. So it is strange fruit indeed, when one finds that a certain way of reading the law is employed one way in one instance, (to protect religious freedom) but is then entirely discarded later on, leaving the right to vote for so many, dangling from a tree.
*I do not practice voting rights law, or constitutional law. Outside of law school, I have not studied these matters in-depth. Just as you should question doctors whose views seem questionable, so too should you question any given lawyer's views. A law degree does not make one smart or wise. To the contrary, many of us are dumb. : )