There is ample reason to conclude that "non-commercial" would include a church, as well as advocating a political cause or candidate. The hard part of "personal". In the context of (Canadian) bankruptcy law, it can mean "non-business use"; in the context of "personal use property", it can be "A type of property that an individual does not use for business purposes or hold as an investment. In other words, property that an individual owns for personal enjoyment". US tax law takes "personal purposes" to refer to non-business purposes. But in the context of copyright (especially music downloading / copying), it is taken to refer to the use of or by an individual. Distributing free copies of a protected work does not get legally sanctioned due to the copying being non-commercial.
The alternative term "private" is much clearer, in identifying "just you", but is probably avoided in this kind of context so as to avoid the wrong inference that you can only play Pokemon in the privacy of your own home. So the slightly less clear term "personal" is used instead of "private" especially in copyright-related contexts. "Personal" and "private" are not exactly the same, but when it's about use, I don't see any difference, and I think there is no question that use to attract to a church or political candidate is not "private", it is public.
Since the license does not define "your own personal purposes" and there is not an existing crystal-clear definition of "personal purposes", the phrase could be given its "ordinary (plain) meaning". Of course, plain meaning has to give way to contractual intent, so we have to figure out what the parties intended. Except, you don't have a contract with Niantic, but still, plain meaning surely has some place in the law of licenses. At this point, in a lawsuit, both sides would hire an expert witness like a linguist or English teacher to make the case that a church or other non-commercial non-private use is / is not included in the meaning of "personal purpose". A silly argument could be made to the effect that if you personally have an interest in doing something then it is a personal purpose (if specifically commercial, it would be precluded by the term "noncommercial"). What makes this silly is that everybody does things for personal purposes (even acting in a way that benefits others, since you do so for the personal reason that you should do so), and thus "personal" would not mean anything. That is, "personal purposes" does not mean "whatever motivation or interest you personally have".
You can also gain a certain understanding of what "personal purposes" means by looking at similar licenses. In the context of academic publishing, authors are typically granted license to copy "for personal, professional, or teaching purposes". Professional purposes and teaching purposes are things that the person has an interest in, so by mentioning these things separately, we must conclude that "teaching" is not a "personal purpose". And so: I would conclude that a court could find that using a product to support a political campaign, philosophy, or religion, is a "public" purpose, not a "personal" purpose.
At the same time, at least as I understand it, a lure module is a thing that others besides yourself personally can see (I admit, I don't go), which implies that the purpose of the thing is not entirely private. In addition, there is a fair amount of buzz out there about how a lure could be good for business, which is (1) clearly in contradiction of the license terms and (2) clearly a golden opportunity for Niantic, perhaps in a few weeks after everybody gets hooked and then they will offer non-personal licenses. Their license terms also say that you will not "use the Services or Content, or any portion thereof, for any commercial purpose or for the benefit of any third party or in a manner not permitted by these Terms". I would say that that definitively says "No don't do it", and it also means that you can't be nice to a neighbor. So what they literally say and what they really intend are probably completely different things.