Fallout – Are there infinite side-quests in Fallout 4

It sounds like this might not have worked out exactly as the developers planned it, which is not shocking in a Fallout game, but the Institute's hostility is likely due to your character's attitude.

Try loading a save before entering the Institute and being a bit more agreeable. This should prevent them from becoming hostile.

Yes, you can get ballistic weave without aligning with the Railroad past the point of no return. Based on my experience and the Fallout Wiki page on Ballistic Weave, you have to complete two quests (Boston After Dark from Dr. Carrington and Mercer Safehouse from P.A.M.) to unlock the Railroad radiant quest, "Jackpot: {Location}".

The Jackpot quests are given by P.A.M. There are three locations these quests can send you to.

1. Hub 360
2. Medford Memorial Hospital
3. Pinnacle Highrise

After finishing one of these quests, you might be prompted to talk to Tinker Tom about Ballistic Fiber technology found in the cache you recovered. If not, you'll have to continue with the next Jackpot quest.

Most importantly, all of these quests are available before alignment needs to be chosen. The only quest of this chain that actually had any true Railroad story or impact is Boston After Dark (and the prerequisite quest, Tradecraft). Mercer Safehouse is a simple settlement establishment quest, and Jackpot quests are radiant fetch quests.