I'm not sure I understand your position very well. Of course I think everyone has a right to believe whatever they want. But they don't have the right to inject their beliefs into politics, curtailing the rights of women, LGBT people, and other minorities, as they manifestly have done for decades.
You say I wouldn't feel comfortable hanging around should I be the sort of person who says what I think about these issues. If that were because churches were non-political spaces (like some neighborhood bars), that might be fine. But the point of my comment was that evangelical (and some other) churches have become heavily politicized spaces. The rules are, in fact, that you can say whatever you want, as long it agrees with extreme right-wing conservative dogma. In many (especially smaller) evangelical churches, you'll even hear it from the pulpit on Sunday. As it happens, I just visited the "Bible Belt" and got to hear evangelical Christians trash my so-called "environmentalism" (I tried to recycle plastic).
> On the flip side, evengilical churches do a great job of feeding the hungry, digging wells where they are needed, helping with disaster relief, etc. These are really important works, and given without care for the beliefs of the recipient.
Here again I must say my experience (I grew up in an evangelical church) doesn't match this. In my experience, churches treat these like mission opportunities. Any charity given is closely tied to the recipient's willingness to listen to the Gospel. And that's even putting aside the extremely questionable organizations that often run these programs, like groups tied to Franklin Graham.