Well, let's see...Why not throw my two cents in?
If I invite someone to a social function at church, I'm not in any way trying to get them to attend. Our social functions are purely social. There is no prayer. There is no literature handed out on our church. There is no filling out of forms. There is no one walking around and asking if you attend or trying to get you to attend. I DO invite people to these events, and I don't even know if they are christian. I simply think they might like them.
Then there are the invents that are christian based. Here there may or may not be a form to fill out. Usually not. Still no literature passed out. About all anyone is going to do is say a prayer and have a godly focus. I would invite someone who I thought might enjoy the event (usually it is a speaker of some type) and I know is christian. But not to get them to join our church. And no one is going to approach them about joining either. No one will show up at your house or phone you. You might get something in the mail announcing the next such event if you filled out a form--but nothing else. You know, you saw speaker X. When speaker Y is coming, you'll get a postcard saying speaker Y is coming and when--period.
Now if I thought someone might like our church and they are looking for a church, I will invite them to a weekend service. You still won't get approached in any way from our church unless you fill out a form requesting to be contacted, which is in every church bulletin. And hardly deceptive. Heck, our church asks visitors to refrain from giving in the offering basket--for regular attenders only.
Part of what I love about our church (in the south) is that it is sooooo low key. It has a lot going on all the time, but is never trying to push anyone into joining or giving. Our church does not even do fundraisers. Everything is donated or comes from the offering. When our church was started about 12 years ago, it was started to intentionally do away with what people didn't like about church--based on a huge survey that was done at the time. People didn't like to dress up, so our church is casual (yes, many wear shorts & t-shirts). Our music is upbeat. No asking for money at every turn. No high pressure tatics to join. We have 4 Sunday services (one that does offer the traditional music) and a Saturday service so no one would even know if you were a member or not.
Anyhow, I don't think your neighbors are trying to push you into joining. Maybe they want to introduce you to their church if they never ask you to do ANYTHING else, but again, I doubt it's a membership drive. Maybe I'm being egocentric though. If anyone does approach you, simply say what I say to those mormans that show up at my door--"We have a church that we love & are involved in, thank you." It's polite and to the point. They just say "ok" and walk away.