Sorry, this is kind of long, but it's got a lot of good substance that I hope helps flesh out the inherent flaw in the Trump team's litigation.

I totally agree about voting rights, however their construction under the Constitution is very state-centered. We try to shy away from federal intervention as much as we can. For instance, in Shelby County v. Holder the Court explicitly struck down the Voting Rights Act's Sec. 4(b) formula for federal preclearance on concerns over federalism. However, Shelby isn't directly responsive to this, I'm just citing it to show that the federal government likes to stay out of state voting as much as possible.

There's a marked difference between the "left-wing" and "right-wing" patriots' positions. Bear in mind that, prior to the Reconstruction Era, there was no inalienable right to vote. Until that time, states were free to determine voting standards, largely, as they wished. The only instruction came from Article II, Sec. 1:

Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress

This changed with the addition of the 15th Amendment. However, it is important to note that this Amendment only guaranteed that the right "to vote shall not be denied or abridged by the United states or by any State on account of race, color, or previous condition of servitude." This was extended to sex via the 19th Amendment, poll taxes via the 24th Amendment, and above-18 age via the 26th Amendment.

Outside of these proscriptions, however, there is not much else in the Constitution about voting. Thus, while you have an undeniable right to vote in these protected classes (the left-wing patriot's position) it does not necessarily follow that you have a right to a certain value in your vote (the right-wing patriot's position).

Of course, the response to this is the 14th Amendment's equal protection clause, which guarantees that no state shall "deny to any person within its jurisdiction the equal protection of the laws." This is why in Bush v. Gore the Court struck down the recount on equal protection grounds, as some Florida counties were excluding and correcting votes on different grounds than other Florida counties; the votes in Florida were definitionally being subjected to unequal protection within the state. Of foremost note, a citizen of State A is not protected via State B's laws (assuming the citizen is operating entirely in State A), this is why the Texas lawsuit failed for lack of standing. Now, when a citizen of State A wants to challenge State A's election law, it gets a little more complicated...

Prior to 2008, the Court applied strict scrutiny to state-internal election law challenges. This means that, for any law restricting the right to vote, the state had to present a compelling interest that justified its use. However, the Court decided (in Crawford v. Marion County Election Bd. (2008)) that equal protection analysis of voting laws requires only a balancing of the interests of voters against the interests of the state, which is more akin to something we call rational basis review. The upshot of this decision has been more state laws requiring voter ID, as well as less judicial decisions overturning state election law. The right-wing patriot's constitutional argument is even weaker here, as the underlying logic requires the inference that a law (e.g., mail-in voting) that they are not restricted by has indirectly subjected them to unequal protection under the law. This is what's called a "disparate impact" argument and we've rejected its application to facially neutral laws (see Washington v. Davis (1976)), which is what a law simply permitting mail-in voting writ-large would be.

Thus, what the right-wing patriot is left with is essentially rational basis review. I can cite a whole trove of cases for this, but the short of it is that the state always prevails in rational basis review as long as it can offer some non-prohibited reason for its law (see generally, Railway Express v. New York (1949)). Promoting voter participation is one of those permissible reasons. This is all, of course, guided by the remaining Article II, Sec. 1 deference to states to make their own voting law, as well as the post-Shelby policy for such. In short, the right-wing patriot has no constitutional argument regarding the dilution of his or her vote via their state permitting mail-in voting.