The religious institution existed first. It has a meaning. If you want to randomly change what words when why not start calling oak trees pine trees...they are both trees, after all.
Here is an example I think everyone can understand, and it uses trees:
Hetero union = oak tree
Homo union = pine tree
A oak and a pine are both trees, but they are not the same thing so they have different names.
Hetero and homo unions are both unions, but they are not the same thing so they have different names.
Hetero union is called marriage. But since that word is already taken, we cannot use it for something different, even if similiar. A new name is needed OR we remove the naming altogether and simply just have unions.