It really does, it means that you would support the most right-wing and reactionary british PM ever, which means you would support right-wing republican presidents, meaning you're probably a republican.
If you support thatcher, there's no fathomable reason why you'd oppose Trump anyway.
Didn't you, for an extended period of time, support Trump? I don't think you'd appreciate such deductive reasoning applied to you, would you?
I would've supported Alliance from the perspective of an American. Labour under Foot would not have represented the best interests of Americans (leaving the EEC and cancelling Trident come to mind), and I don't see why some people believe that a party in one country occupies the same ideological space as a party in another, even if they are the most analogous the way UK Labour and U.S. Democrats are.
What parties people support internationally isn't even particularly important, but people also have different values when it comes to the politics of countries not of their own.