I believe it's reasonable, anytime ANY public figure openly supports a political figure, that they should expect candid questions as to WHY they supported that politician? They must consider it to be fair game to be pressed on what exactly appeals to them about that politician's platform...by virtue of the fact that they are using their own platform to promote that politician in the first place.
As far as "lists" or "databases" go -- I do have to wonder what the end game is, from the perspectives of those who'd be compiling those inventories. Do they want formal apologies from a political figure's supporters? Do they want expanded dialogue? What are the tangible and intangible benefits of such lists/databases?
BTW, I'd extend this question to those who are openly endorsing any politician...even though Trump has clearly been the most openly horrific and controversial, in terms of presidential politics.