I honestly think there are two main issues involved here:
1) an aversion to nuance - many people (conservatives in particular) find it easier to view the world as black and white. Thinking about things that fall in between is a lot of effort and, in some cases, may threaten their world-view,
2) an element of homophobia that stems from a very narrow definition of masculinity and what it means to be male (see #1 above) - men fear being 'tricked' by a 'guy in a dress', which would make them 'gay'.
Yep. See #1 above.
If you can gain the vote of an entire constituency by taking a stand on one issue, it may be worth it. Politicians are, after all, opportunists.