I've been researching genealogy for about 20 years and made extensive use of LDS resources through their Family History Centers (I've been to four different centers in the country), their PAF software, and recently their web resources.

I'm not Mormon, but never once while I was in a FHC did staff or patrons mention their religion or ask about mine, never asked who I was, what I was researching or why. They never interjected any religious doctrine into conversations or into my research, or tried to influence my research, and there was never even a hint of quid pro quo for my use of their genealogical resources or facilities.

That's my experience, anyway, and I'd be surprised if they were using the Ancestry.com site to further any kind of doctrine.