just saw this thread and thought i would way in
Disclaimer:I am a Christian
1. The BYU and the ND comparison are a little different i think in terms of the religiosity, In the US, there are more Christians then Mormons(fact--not debating merits/religious aspect, just by pure numbers). As well, there are more "Christian" schools then "Mormon" ones. For Christian/Catholic bents, one has numerous undergrads to choose from as well as some law schools(ND,Regent, St Thomas(Florida and Minn), Ave Maria, Catholic University, Texas Wesleyan(?), SMU(?),Pontifical Catholic, Roger Williams etc). For Mormons, especially for law school, they really have the choice of BYU, or Utah to a much lesser extent. As such, I would expect BYU(especially with their Religious bent honor code) to be a lot more "religious"...At the same time, especially with law school, any ABA accredited school has to teach certain classes. So, any school can only be "religious" to some degree. Overall, I do not feel the BYU to ND comparison is that fair since ND is one of a few Catholic institutions while BYU is the only "official" one (Also, the Church of Latter-Day Saints funds BYU--Does the Catholic Church help fund Notre Dame--I do not know the answer to this question).
2. You have to keep in mind that your law school experience will be tons different then undergrad. For one, you most likely won't be living on campus. As such, your immersion into the campus culture won't be much outside of classes and student involvement(and the latter you have complete control over what you get involved in). With Law school, you will have very little free time in all likelihood, so a lot of your time will be in the library, you apartment etc. You certainly will not be forced to partake in much of the religious aspect of the school. With any experience/school, it will be what you make of it. Can you go to chapel at ND if you want? Of course...but you also can not go to chapel and you won't be shamed or anything.
3. At ANY law school you attend, there will be religious nuts, there will be the tolerantly religious, neutral, tolerantly athiest and athiest nuts. That is nothing more though then a commentary on our society and how diverse it is--You might get a little more of it at a ND or a BYU type of school, but I doubt it would be significantly more, if at all. As a result, unless you hugely worry about the religious dimension, it should not have a big effect on what law school you attend. Remember, you are going to law school to get a job, have a career etc. Three years of your life is not that long in comparison then if the school you choose is "better"(by any subjective argument) and will result in "better" career choices for you. The key question then, after hearing from many TLSers and visiting ND is to ask A. "Is ND or Minnesota a better choice for my career goals"? and B(to a much lesser extent), "Would I be happy with either school"?. As well, given the small ranking difference(though ND has more lay prestige as has been said), you also need to ask "In what environment will i succeed more academically?".
4. In your case, in reading the entire thread, I think it's become quite obvious that you believe the religious dimension to be a significant issue, and it seems like it is a bigger issue to you then the issue of career prospects. You have a stereotype on what Catholics are (like any generalization, it is definitely not 100 percent true) like. There is a talk from NDers that there are crucifixes and occasional prayers and these(in the grand scheme of things) seem to be a huge issue for you--It seems like it is hard for you to get away from that stereotype and those small displays of religiosity to an extent where it may hurt your ability to focus in law school. You see the religious/belief differences as so much of an issue that I do not think it makes sense for you to attend ND. Consequently, with all the information on this thread, I think you need to attend Minnesota.