"I have been told in other places, "You can't believe 'that' if you want to worship here"
That's appalling. It's the people who 'believe' incorrectly we should most WANT to "worship here." I've gone to a lot of churches over the last 7 decades but I've never known of any church leader expressing that thought.
I have known of a few churches, including the one I'm in now, properly requiring that anyone applying for membership agree to specific points of doctrine and not cause internal strife before officially joining but I've NEVER heard of anyone demanding that people agree to such standards for attending and fully participating in local church activities. (Formal membership should be required for voting, teaching and holding most church offices tho.)
In fact, we have a couple who have attended for some 20 years without joining because the husband holds some strange idea that the Trinity isn't what scripture says but they are fully a part of our church family in every possible, non-member, way. We love them as part of our church family, they have received pastoral and congregational support during times of trouble and, to the best of my knowledge, NO ONE has every confronted them in any inappropriate way for what they incorrectly believe. And, IF that ever happened - and was known - it's highly probable the elders would visit the attacker for Godly correction; that IS part of the elder's shepherding duty, before God! (see Jer 23 and Ezk 34)