AnthonyGA:
To compare the a person's clothing to skin color and nationality is really apples and oranges.
When entering St peter's in Rome, you would be in Vatican CIty, which is completely governed by the Roman Catholic Church. This is not a "perception", but a fact. You are on Church property anywhere in the Vatican.
To be more serious, I believe this is a question of the perception of modesty and respect according to the rules of the house, not tax dollars.
And anyway, the line between the Church and the state is very blurred in Italian life.
I might be wrong, but I also don't believe that a Jew wearing a yarmulke, a Sikh wearing a Turban, or anyone dressed to reflect their personal religion and observing respectful behavior would be bothered in an Italian Church.

Where would I draw the line? I wouldn't draw any line. If I wanted to visit St Peter's, I would cover my shoulders. If it were some other place in another culture considered sacred or a house of God, I would do whatever was required to show respect as a visitor.

And I think that if it's a matter of huge importance that I wanted the freedom to wear whatever I please, as you describe, I would simply find my entertainment in places where this is not an issue, such as a Museum. Here at home, I have a vote, and the right to complain loudly. As a visitor in another country, in a church, I would not bring this expectation along with me, and would behave according to local custom or rules of the house.

AntonyGA, it is a question of covering up one's pride, not one's skin colour or religion. The idea is that one is supposed to at least appear humble on the outside when entering a house of worship.

Thus, AntonyGA, if the door guard knows his job, he will ask men to remove their hats if those hats denote nonreligious status or occupation of some kind, e.g. military headgear or (in another century) top hats. I doubt a yarmulke must be removed as such head covering is part of an observance of God, even if in a religion other than Catholicism. Ball caps, on the other hand, while not necessarily denoting status, do have a certain frivolous air about them, and a church is supposed to be a solemn place.

The question of women's head coverings is more complex. At one time hair was considered an object of pride in women - there's even a biblical verse along the lines of, a woman's hair is the glory of her head. Thus the one-time prevalence of head scarves on Catholic women attending church. Perhaps now that women wear their hair short, it's less of an issue.

Not all door guards are consistent. On the other hand, the ones I've encountered made no distinction between gender or age with respect to shorts.

As for how far one is willing to bend over, I think you're trolling here. In any case, if you are peeved by restrictions, I suggest you not try to visit a mosque - that's if they let you in at all.