It seems offensive to say I would go to a Mosque for the purpose of trying to convert them to another religion. That is just rude to invade someone else's space that way. So I think many Democrats would find the comment unacceptable - and stupid. Some Pubs would too, but far fewer. Do you plan to go a Mosque for the purpose of trying to wean them away from their religion? If I were running the show there, I would tell you that your role while there is to be seen, not heard.
Democrats would find it unacceptable? In 2012 I heard about some hipster Christians were lit dropping liberal Christian pamphlets at mosques and Catholic/Mormon/fundamentalist churches about how they were evil if they supported the gay marriage ban in the Twin Cities. How much would you wager these people are Democrats?
That is not trying to convert them to Christianity. And it is dropping off paper, not approaching people, to boot. Surely you understand the difference don't you? You don't proselytize in someone else's house of worship. You just don't.