Is there a way to build it without joining the 3 optional factions? I want to join the institute so that means going there free of any alliance with the other factions. The game won't let me build the interceptor and every faction leader wont help unless I join them.

Bump. Would really like some info on this

You need to teleport into the institute before you can join them that means at least interacting with the rail road.

I have interacted with everyone but unless I join them they won't help me. Preston is the absolute worst because unles I become his damn leader he won't help.

Well minuteman can coexist with any faction(with some charsima checks) so you can always join em and institute.

In the Institute missions you need to join then betray the railroad