You are right that they do have that prerogative according to U.S. Law, but a church that did that would be doing great violence to the gospel and severely hindering their own witness to the lost by requiring such a thing. If It's not called legalism, fine, but it's something bad.
That is the equivalent of saying that those churches who have schools that require uniforms for their students "are severely hindering their own witness and doing great violence to the gospel." Nonsense. My example was just a bit more extreme to catch your attention.
I know churches that require their women to cover their heads.
I knew a preacher some time ago that would not allow anyone to preach in his pulpit that word wire-rim glasses.
Many years ago I knew a man who would not admit into membership women who would not agree to not wear jewelry or pants. (another generation.) This was an exceptional case. There were many other churches at the same time that preached it from the pulpit and would hold the same standard (at least for pants on women) for those in leadership. For others it had to be by conviction and usually it ended up being 100% anyway.
In all of the above the gospel was never hindered. Your reaction is an over-reaction.
Here's my 2 issues:
1. If the word legalism applies only to requiring extra works for salvation, then what word would describe requiring obedience to extra-biblical standards for one to be considered an "obedient" Christian.
The issue has nothing to do with legalism.
If you believe my standards are "extra-biblical," then I probably don''t. I would probably view you as having standards that are worldly. The issue is therefore: worldliness vs. holiness. It is summed up in Romans 14, "Let every man be fully persuaded in his own mind." If you are fully persuaded in your own mind that it is perfectly acceptable for your wife to go to church in a halter top and skin-tight jeans then you will stand God for allowing her to do so. You are the head of your house. For me, I see it as sin. It is not modest, and that is what the Bible demands. Again the issue is worldliness vs. holiness.
2. And, even if one does not push their beliefs on others,
If your wife wears a halter top to church, I am not going to PUSH my beliefs on her. I trust that she would be convicted by the Holy Spirit not to dress that way again. We don't have such rules. We have standards for those who are going to be on the platform, so dressing like that would eliminate her from singing in a choir or doing a solo, etc. She could not be a representative of the church in any way dressed like that.
If a person believes that something is a sin, that the Bible does not call a sin; are they a legalist, or is it something else?
The Bible doesn't call halter tops sin. But I do. Are you going to come to my church and argue with me over it? So it is with many other such issues. Thus they are left to each autonomous local church to decide for themselves where to draw the line. It is up to pastor to teach these things.
If I believed I had to open doors with my right hand only, because my right hand is my dominant hand, and I want to give my best to God, am I a legalist?
No, but you would be different. There is nothing wrong with you opening the door with simply your right hand. I am sure that many people do just out of habit.
If we don't use that name, is there any grounds for a fellow believer to come along and say, "You are just wrong about that! God would be just as pleased with you using your left hand...or wearing blue...or playing with cards...or letting your wife wear pants." ???
I have a reasonable explanation for the things that I do. My decisions are not made in vain.