I understand that the BoS, Railroad and Institute all have completely incopatible goals, but what about the Minutemen? Do they become hostile if / when I side with one of the others? And if so what does that mean for all the settlements I've built up, especially The Castle?

Not looking for major spoilers here, just want to know if I can side with someone else and keep my artillery support

The minuteman don't plan on exterminating any other faction apart from the Institute. However, they can destroy the BOS if you make the BOS hostile for any reason.

However, Preston gets angry with you if you sided with the Institute and don't pass a charisma check or he will call you a mass murderer if you never activate the evacuation sequence. All this means is you can't recruit him. Don't know if this means you can activate the minutemen flare or artillery strikes.

So my takeaway from this is that as long as I don't go full Institute I'll stay good with the Minutemen.

Thanks!