Having a shrine is not illegal. That's a psychological issue. The actions that are illegal are those which directly impact the victim and the law deals with those in respect to the extent it affects the victim.

I am not expecting the police to be uber helpful (they have limited resources and legal guidelines of their own to work within) but sometimes the mere fact that you have talked to them can make you feel better and also gives you some ammunition to use. They also have personnel who deal with this sort of thing every day and so know how to deal with it.

This guy sounds like he is certainly suffering from social and/or psychological problems - maybe a form of autism, maybe grief due to the loss of his wife, maybe something else entirely. He may not even be aware that his actions are causing distress and he may not even intend any harm at all. However, it has you concerned and so it is a problem. I don't think this is going to be resolved without external help.