You actually have it backwards. Unionized productions aren't limited to unionized crew; in fact working on unionized productions is how you qualify to become a union member. OTOH, union members are generally prohibited from working on non-union productions. IOW, it's the opposite of gate-keeping.
It sounds like you and your friends tried to get hired as crew onto jobs for which you have no experience, because if you guys did have the experience you would already be union members and you would be swamped with work or offers. (The thresholds are pretty low. I'm one production away from being a member of several unions and I'm trying very hard to avoid that since it would limit my ability to work on non-union productions).
Most jobs don't hire people without experience without someone vouching for them. Why would you think that Hollywood would be different? They don't know you from Adam and from their point of view there are millions of other people just like you that are willing to put in the time and effort to start at the bottom instead of trying to skip a few rungs.
If you want to work in film, start at the bottom (i.e., meaning as an assistant or an extra) or work non-unionized productions (generally, low-budget or student films).