I allowed my kids to apply where they wanted. There were some I wouldn’t have wanted them to attend due to numerous factors, and I shared some of those sentiments, but they made the final choice of where to apply. In the end, I fully supported my D’s choice but not my son’s, at first. I shared my concerns, told him why I thought another school was a better choice for him, but ultimately allowed him to go to his first choice. I’ve really come to see that he chose the best school for himself, and so far he is doing great and very happy.
I don’t think any of the reasons you mentioned would make me forbid a child from attending. I think you probably have a right to veto based on location because travel can add to cost of attendance. I know quite a few parents who have given their kids a radius that they must stay within. Certainly within driving distance of home there should be a ton of great options. However, if my kid had a valid reason for choosing a school very far away, I might change my mind. Few religious schools would give me pause. Most have non religious students that attend. Interestingly, the school my son is at had a hurricane his first week in. We are NOT in an area where that is really common. Things like that can literally happen anywhere.