Yes, they should.
The HOF is not just about your playing abilities (although it mainly is), it is also about your contribution to the game of baseball.
His "views" and how vocal he is about them are detrimental to the sport. He should not be honored for being a shitty ambassador.
To be clear, I do not think him being a conspiracy theorist affects the MLB's bottom line. However, he is closely associated with baseball and him being paranoid about the Deep State and other stupid stuff makes the conversation about "former baseball player Curt Schilling"... you do not want to taint your HOF by having the conversation be "baseball hall of famer Curt Schilling thinks some elected officials should be hanged".
Never forget that a HOF is not strictly about honoring the game, it is mostly a business and a way to sell the game. It is marketing. Associating yourself with Curt Schilling is bad marketing. His "brand" is toxic.
And, once again, I must repeat, your euphemism about "political views" pushes the real issue aside. Nobody would be blaming Schilling if he was a normal conservative. He is being being vilified for spreading conspiracy theories and advocating some people being killed. He is a nut-job. He does not deserve publicity and acknowledgement. As a public figure, as a representative of baseball, he has a social responsibility; he is clearly failing BADLY at that. If you think his views are acceptable in a civilized society and that we should accept spreading hate/lies/conspiracy theories, well, that's another debate and we are not allowed to have it here (another debate we are unfortunately not allowed to have is how some people misinterpret the first amendment/freedom of speach in order to spew their bs).
Is Curt Schilling a HOF-caliber pitcher, yes. Should he be in the HOF, no.