Is working for the Railroad the only way to get access to the Ballistic under armor. I dont remember my first playthrough with my pro institute character ever gaining access to it. (She wiped out the Railroad as soon as she found them, didnt even wait to encounter Shaun)

Yes. It's a railroad exclusive item. However you don't have to side with them completely, just do the cache quests for PAM then you should get it after 3 quests or so. However if your on PC you could probably use the console to get it

Ok, does the BOS or Institute have a similar thing? Do they have items you can only get by joining their factions? Kinda strange that only the Railroad gets a special set of armor.

Brotherhood allows you to call in a vertabird mounted with a mini gun to take you to any location you have discovered

Minute men gives you flares and a flare gun to call in ground support and a smoke grenade that launches an air strike if you have the artillery built at a settlement and are within range, you also need a settler assigned to the artillery

The Brotherhood offers a Unique/Legendary set of T-60 power armor.

As we are in the spoiler forum, you can get this from the RR as well if you follow the quest line to the end...

What is the cache quests?

PAM will send you to unlock a DIA cache after you do her first task of setting up a safehouse. After you uncover the cache and report back to PAM talk to Tinker Tom and he'll talk about the BW. Once that's done you should be able to use BW yourself at a crafting station.

The first one PAM sent me to was to just find some note in a hidden spot, which led me to another note in another hidden spot, and then report back.

The Ballistic Weave is really overpowered though, especially if you're Armor Perk is rank 3 or 4 and you put the weave on an outfit and a hat. I'm guessing that since the RR does a lot of their work undercover that they generally work dressed in regular outfits, not all decked out like a merc, so the weave helps them in that regard. The fact that you can wear the weave, on an outfit and hat, and then put a full suit of armor on top of that (depending on the outfit allowing it) just makes it way OP.

I'm using it in this play-through as it's my RR run, but after this I doubt if I use it again. I'm also considering not allowing my PC to wear any armor with it (though I love my shadow armor ... and the Deep Pocket's mod on each piece).

Every faction offers something, but nothing nearly as OP as ballistic weave. You can use it on army fatigues and battered fedora to get 220 defense. You can wear heavy combat armor on top of all that to get ~340 defense. At that point, there isn't much that is a threat to you.... particularly if you add a bit of lead shielding and find a few poison resist armor pieces. You'll still want a hazmat suit, rad-X, or power armor for heavy radiation though. As others have said, you don't have to side with the faction...just do a few quests.

Yeah, I suspect it was only ever meant to go on regular outfits that take up most armor slots. Almost all of the clothing options that allow weave are like that. It only works on a couple hats and under-outfits...which seems like a mistake. If it was meant to work on that kind of thing, I'd expect they'd have tagged a lot more of the hats and under-outfits. This seems like dev laziness rather than an intended situation. If it was done that way, the best combinations would hit ~160 armor I think, which puts it more in line regular armor use and makes ballistic weave seem much less required.

If you're on PC, you might as well throw in mods to allow arbitrary armor layering and ballistic weave use, and then use as much armor as you feel fair, since the default state already allows for insane OP armor anyway. In my current playthrough, I'm not using ballistic weave at all on myself... but I've layered heavy combat armor (dark metallic re-textured) with the silver shroud outfit. It looks amazing and has me at about 200 def overall, pretty well short of the default 340 mark I could hit by default. It still feels a little OP, but heavy hitters can still knock a good chunk of my health out. I tend to put weave on companion outfits (best use of weave IMO) and sometimes on outfits for special settlers. Vault-Tech guy gets a 110 weaved clean black suit and a 110 weaved bowler hat.