Well, My convictions certainly don't line up with what is considered Baptist Theology, though i go to a Baptist Church. Mine line up more closely to Lutheran.
There probably will be some that say sure, in Baptist churches. The odds are not in their favor. But i want to answer these individually.
1. Tolerance of other faiths: Showing love towards other faiths is very much a Scriptural stance. The word "tolerance" throws me off a bit because it implies, to me at least, truth is subjective. However loving other faiths does mean giving other faiths the right to be had. If tolerance you mean that, then sure. If you mean to imply other faiths are equally valid to be true, then you might be looking for a liberal church which doesn't take Scripture to mean what it says.
2. People's rights to their own life style: Well my opinion on this is probably going to differ a bit than most. Sure people have rights to their own lifestyle. People, civily, have rights to marriages if they are gay by law. But as of Scriptural foundation, it is a person who wants to be a Christian must repent of they are in that lifestyle. They must take themselves out of that lifestyle. If they don't, they should be anathematized from the church and hand them over to God, and disassociate with them (not out of hate, but love). But people's rights? Sure.
3. ok to base your walk largely on your own convictions: That depends. your own conviction in cars? no prob. Personally convictions, meaning spiritual beliefs are subjective to ones personal experience? You might want to find a unitarian universalist church where there are basically no rules to worry about.
Not trying to be mean at all. I just figured you wanted to some answers that were truthful and direct you to locations your heart might be at.