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https://www.breitbart.com/politics/2019/03/17/washington-senate-passes-bill-eeping-trump-off-2020-ballot-until-he-releases-tax-returns
State can have almost any restrictions or requirements they want for federal office candidates. The Constitution only sets minimal requirements; the states can add whatever they want. (If they tried to prevent black people from being on the ballot due to their skin color, or a gender requirement, they would fun afoul of the Constitution. But as long as it's not illegal discrimination against a federally protected special class, they can discriminate all day long.)
Every state already has a shit-ton of requirements and restrictions about who can be on federal ballots.
For the Presidential office, don't forget that the candidates on your ballot
are not even who you are voting for! You are voting for the ELECTOR who has
claimed that THEY will vote for the candidate. The state also determines,
in whatever manner it chooses, who the ELECTORs will be. And they can and do
pass laws specifying how those electors will vote for President. (If the elector
doesn't do what the state ordered them to do, they can go to prison or be
sentenced to death or whatever under state law.)
There is nothing in the Constitution that directly gives individuals a
vote for President. It is only the electors. There does not need to
be any statewide election where citizens cast a vote on any ballot.
A state is free to use any process they want. For example, a state
could decide that the Governor will choose the electors and that
the Governor will instruct them for whom to vote in the Electoral College,
and that if they do not vote that way, they will be shot on sight.
The idea is that the states are the power, and that they are controlled
by their citizens (for example, choosing their Governor somehow).
Individual citizens DO NOT HAVE ANY VOTE under the Constitution.
You may find that shocking.
It's not how everybody thinks any of it works.
But it is exactly how it works.
Anyway, YES, states CAN AND DO arbitrarily determine who can be on the ballot.
It is all controlled by state law.
Under the US Constitution, there don't even have to BE any ballots or anything!
This is why Trump will not be on the ballot in a number of states in 2020.
If the red states can contrive something that is legal enough under
their own state laws to exclude Democrats, they can play that game, too.
However, this game is only meaningful in swing states; it wouldn't do
anything in states that are controlled by Republicans.
The swing states where it does matter just happen to be
controlled by Trump haters, though.
This is how Trump will lose in 2020.