The rules for that status are the same for all institutions, religious or secular.

If a particular religion, by its organized teachings, or a particular house of worship, by its clergy's actions, break those rules, the organization is reclassified as a political organization, and their special tax status goes out the window. Actively seeking, through use of the pulpit and other official means, to affect political actions of any of the congregation, even one member, is one way to break the rules and be reclassified no longer non-taxable.

So, no, it's not establishment to enforce the tax code equally for everyone. That's called "equal treatment under the law". Giving special permission, by decree or by neglectful enforcement, to one denomination or institution to ignore portions of the tax code and still reap the benefits of special status is favoritism and so could be argued to be establishment.

I hadn't thought of that. Thanks for bringing it up!