Yeah, I think it's at least possible to be a nominal Christian/Jew/whatever and be kind of agnostic about the DOYC itself. I mean, if there are actual (closet) atheists employed as ministers, certainly it's possible for people to be regular churchmembers for reasons of community or a want to serve the greater good*. Likewise, I think it's possible to be a believer in some sort of higher power but want nothing to do with the trappings of religion itself. I'm not entirely sure either approach is anathema to skepticism.
And here's the bottom line: there will be exceptions to every rule. If you impose a hard and fast "religion != skepticism" rule, you are guilty of lazy thinking and aren't behaving skeptically. Every claim is different and ought to be discussed on its own merits. If, after hearing the merits of the claim - whether that claim is about a new Bigfoot or about whether or not someone's individual religion/theism is compatible with the worldview of skepticism - it sounds like 20 others that you've already debunked, fine, debunk away. To go into a claim assuming said claim is debunked because it violates a pre-existing rule... well, that's the sort of attitude that gives skeptics a bad name.
I get that people don't want to cloud what it is that skepticism means. I certainly don't want skepticism to mean "apply scientific rigor to everything except Jesus". At the same time, the movement will not grow as long as there is not tolerance for diversity of opinion. That doesn't mean you have to agree with the other person in question. It doesn't even necessarily mean you have to go out of your way to accommodate someone who insists on injecting their non-skeptical belief system into everything. Such a person will probably not find skepticism to be satisfying and will likely leave of their own accord. The flip side is, if you've found common ground with a fellow skeptic, you don't need to castigate them for their religion/belief in UFOs/whatever at the same time.
I want to get back to this point because I think it is really, really important: the most important part of becoming a skeptic is adopting the mindset and the thought processes of a skeptic. It's not believing or not believing in God. It's not understanding the paucity of evidence for UFOs or Bigfoot, or even understanding the crazy logistics involved in a conspiracy large enough to make a faked lunar landing or 9/11 attack plausible. I firmly believe that once a person starts to think skeptically, they'll agree with me about all of those other things as well once they've examined them. However, examination of that type is a personal process and by throwing one field that someone hasn't examined critically yet into their face, you're as likely to drive them away from the skeptical mindset as you are to make them reconsider their position. Of course, *you* will feel better about yourself for having exposed hypocrisy, which is, I suspect, the true reason why people do this sort of thing, but that won't in the end make the world any better, really.
*Not saying that you need to be a member of a church to do this or even if it's the best use of one's time. However, we are only open to options we've experienced.