Well I think that you should be paid for the regular church services at least! My plumber lives a couple of houses down and I wouldn't expect not to pay him because he is "here anyway" . Also, what happens if you retire from your post? Will the new organist be expected ro play for free? Presumably there is a collection during the service. Why should you not be paid part of that?
I've been told that the church doesn't charge for baptisms unlike weddings and funerals, but round here, the vicar does ask for an organist's fee. So the family should still have paid you.My general rule with services is that if I would have been there anyway eg funerals of friends, church members etc, I don't take a fee. I don't get paid for playing at my own Methodist church and that's fine because I attend anyway.
If we don't value what we do why should anyone else? The churches are really taking advantage of people - pay your musicians for the work they do for you!