I've used it several times on styrene and vinyl and it has never made a kit fall apart...and one of those kits was my DS9 station; a kit that doesn't have a lot of strong gluing points; which I painted and stripped THREE TIMES.
Make sure you wear your rubber gloves and breath mask though, and work outside, if possible.
I've used Easy-Off™ Oven Cleaner on a dozen or so models and it's never eaten them up in any way. Takes the paint off, tho you sometimes have to do multiple applications. It's taken only a couple of models apart and they were built using Tube Glue (prolly Testor's brand, tho I don't recall for sure).
* Work in a well-ventilated area.
* Wear some sort of goggles/safety glasses and a respirator, if possible.
* Wear cleanings gloves, of the type used for cleaning with bleach and/or for oven cleaning.
* Wear cold clothes!
I once let a model sit in Easy-Off™ for more than 4 months (forgot about it before going on a deployment) and it didn't cause any problems. No brittle plastic or anything. Also works well on resin kits/parts.
A possible sub for the Easy-Off is Scrubbing Bubbles™. I've heard good things about it, tho have yet to use it. Definite plus: the fumes aren't nearly so strong!
So you know, the Fumeless kind seems to not work as well. Don't know why, but the old fashioned type of Easy Off seems to do the best. Just in case you are buying some, see that they have fumeless, and think it may be better then going through the trouble of trying to ventilate the area you are working.