I come from a close-knit church family; I have enjoyed many dinners, game nights, and group service projects with them. I am one of the few singles in the midst of many couples and families, and 99% of the time, that's just fine.
Some families within the church have asked me to babysit on occasion, and I'm happy to do so. I have been involved with children's ministry so their kids know me. If they are going on a date-night or something they usually pay me or arrange some kind of favor in return for my babysitting; if these are (volunteer) church leaders who need a sitter during a meeting, then I usually sit for free. They are at meetings, worship team practice, etc. in order to serve me and the rest of the church; watching their kiddos is a small way to thank them! As I said, my relationships with these people are not limited to babysitting, we enjoy our time together in and out of actual church services in many different ways.
The issue that has come up a few times is when people ask me to babysit during all-church events that I had planned to attend, such as nights of musical worship or our annual church banquet. This feels like a slap in the face to me, as though people don't want my fellowship so much as they want my babysitting services. I understand that these are exhausted parents who are looking forward to a night away from the kids, but as a Single, I am looking forward to a night away from my empty apartment, and as a teacher by day, I am also looking forward to a break from kids during these events! Giving up an evening so friends can enjoy a date night or attend an important meeting is one thing; giving up a church event that I have been looking forward to is a different story. We live in a medium-sized city and I find it hard to believe these parents couldn't find someone from outside our church to babysit for one night.
I doubt these people have intentions of hurting or insulting me when they ask me to babysit during these events. So far, when it has happened, I have had a way to graciously say no, (I am bringing a friend to the event, I am busy that night and wasn't planning on going to the event anyway, etc.), but I'm sure a day will come when my only excuse is, "I am looking forward to an evening with my church family." Would it be horrible for me to just say this when asked?