Dear Mods (and OP): I have been mulling this situation over in my head all morning and would truly like to offer some thoughts to the OP in the hopes of helping her and her son. I see no way to do so without discussing her religion as it pertains to this particular situation. I think this is okay within the DIS guidelines as so far as I understand them, as I feel we are prevented from debating what is right or wrong within religion, but not from a respectful and factual discussion in which it is somewhat involved (at least, that was what I understood as to why prayer requests are allowed). Please accept my sincere apologies if I am misinterpreting this at all, and OP also accept mine if I come across as anything other than respectful; I do not share your beliefs but I am trying to look at this issue from within a framework including them, if that makes sense.
and with that LONG preamble here goes a really, really long post (or series of posts perhaps, to break it up):
OP, your son is 16 1/2. This is an age in which most teen boys are meeting and dating girls. You and he have very restrictive religious beliefs that do not even allow dating (so far as I understand it) only courtship. The church you attend daily and half the Sundays in a given month does not have teens who you or he feel are suitable to spend time with.
Your son attends a Christian school, but others of your faith do not beleive in even teens attending school outside the home, so the kids he goes to school with are not going to share his faith and the girls there (if there are any? IS it co-ed?) will not be of the same courtship mindset or possibly not up to his faith standards.
This means your son really only sees girls his age that he might be able to be interested and have be interested in him two times per month when you go to your home church. That is precious little opportunity for a boy his age. FURTHERMORE, you yourself point out that you are not as conservative in the following of your religion as most. You send your older children (including this son) to private Christian schools, allow them out into the world more, and even went to Disney World, all of which many in your faith disapprove of. This means it is quite possible that the young women in your home church (or their families) do not see your son as having a strong enough or correct faith to consider him for any future relationship. So, it is very possible that so long as he has this faith in this environment he has truly no possibilities of forming romantic relationships of any kind with girls his own age. In effect, xyou have (purely unintentionally, I am sure) put him in a situation where he does not "belong" in any social group with those his age and is likely to be seen as "not suitable" dating/courting material to ANYone he has contact with.
It sounds like the woman is in a similar boat. Pretty much all the men and women in your faith are married long before 28. Most already have kids and are not even going to be easily available to do "friend" things with a 28 year old single person. She probably has virtually no chance to meet potential suitors and extremely few chances to hang out with friends (within the faith) at all.
To some extent, within that context, it seems somewhat "natural" that they have formed a friendship; they have no one else really. On the other hand, it would also be extremely natural under such circumstances for that friendship to develop into more (and I suspect it already has for your DS if not yet for her).
I think you and your DH need to be honest with yourselves about what the two are likely feeling or will feel, and about what the type of isolation your beliefs combined with where you live has done to foster that, then you can begin to address the situation.