They are:
Barrels (+1 to a stat for one person per barrel)
The monthly shrines (+3 to that months stat/resistance for all)
The Temple of the moon (+5 to all stats for everyone, mod a couple of errors)
Decks of Fate (+4 to a stat for one person per deck)

Permanent stats cap at 255 EXCEPT for the decks of fate. They can boost your stats past 255 (probably to a max of 32767). As far as I can work out they are the only things that can do that, and once a given stat is raised past 255 then using any other stat raising method on it will instead drop it back to 255

So, once anyone has any stat past 255 you can no longer complete the Temple of the Moon (without losing the stat). In fact you can't use any altar past the first one that would affect a super-high stat and the only way to get past the door into the final room is to have a beacon set there.

Once anyone has a stat past 255, then you can no longer use the monthly shrine for that stat

And obviously you can't use a barrel that would affect a +255 stat for anyone

Conversely you don't really want to waste those decks raising stats that aren't 255+, you want to store them away until you've maxxed out stats the regular way. Then start supercharging them!

I guess resistances will likely work the same way but I've not got anyones permanent resistances to 255 yet.