I saw last weekend that they just joined my church, which is currently meeting over Zoom. It is a very small group (< 50 families). We just joined a few months ago, so we're still in the process of building social bonds.
This sounds rather interesting. So you join the church and after firing the person, he joined this church of yours? That sounds like a very odd coincidence and it is certainly something to keep an eye on. If he is somehow joining more of your activities, then I would flag it as something you might need to address but at this point, depending on the town size and where this guy lives in relation to the church, I would just write it off as an odd occurrence.
I have been sued by former employees before and it is not fun.
Did any of them win their case? If so, perhaps you should be applying lessons of those events to this one. Did you have clear reasons to fire this employee?
I'm not sure where you live but I'm assuming the USA. If so, nearly every state is at-will employment. That means you can fire them for any reason, for anything. Usually the law is strongly on the side of the business unless they find out you violated federal/state laws concerning employees. That or your employees are contractors and are bounded by the contract but even then most contracts are in favor of the employer than the employees. So if they are winning these cases, which would be very hard to do in USA, then I would look deeper into what you're doing with your business and how you handle employees.
Should I just try to ignore them? Should I pull back from any smaller group activities where I might run into them? Should I leave the group entirely?
I would just continue on as if nothing is going on. It's a simple employment termination and hopefully he find another job. My advice is to just greet him/her and simply carry on without any mention of the termination.
However, if he/she becomes hostile or starts to spread rumor, then I would go the route of either leaving or filing a police report on the matter stating that he joined the church shortly after you firing him and has been harassing you.