How does an adult forcefully move into another adult's house w/o permission?
No more chances. Already your reputation is damaged by the one time.
The neighbors are going to definitely think you're unbalanced if you start setting up counter cult things. It will look like a bizarre war. It seems quite normal to us to put up a counter cult sign or whatever, but that's because our perceptions are not based on a normal religious background.
Try to think of it from a normal person's perspective. A new neighbor moves in and lets her mother move in soon thereafter. The mom starts doing bizarre, annoying things in the front yard. How does daughter react? Not by doing bizarre things in response, but by stopping the bizarre behavior.
Personally I would try to apologize to my neighbors and say her delusion is a sad thing and you're trying to get her help, but until you can sort it out, would they please be patient with her harmless stunts?