Really, it's not that complicated, which leads me to believe you're being argumentative.
Who owns it? The corporation, partnership or sole propriety that is the religious enterprise owns it. There are officers of that corporation and those officers or designees, enjoy the rights that any private property owner enjoys.
If you walk into a church and the parish priest or his designee tells you to leave and you don't leave, you're trespassing. It's not that complicated.
Or maybe many on here post things as fact they can't really substantiate. At the end of my first post, I said the article probably doesn't provide enough information to draw conclusions. I'm sticking with that unless someone provides some specific statutes or court cases that address this as it relates to mosques or churches. There might not be any precedents for this specific circumstance, and I wouldn't wait for those Muslim women to file a law suit to clarify it.
And one can never be certain how a court might rule on such a highly specific set of circumstances as this. I'm calling it a gray area of the law until it's clarified by reference to statutes or a court case.