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?