Would be really weird to play 65 like taht, but not impossible.. I just nit call.

Lets evaluate this further.

We have to look at hands villain is x/raising with AND calling a shove at a high frequency.

So villain has a random bluff like busted diamonds. Calling and raising is the same as he will always fold to a jam. 2 pair would be too loose to raise here. QQ/ 77 are possible, tough they might wanna lead flop or x/raise it some of the time while 65 always just calls.
QQ and 77 should be capable of x/r/fold as your river 3betting range should have them beat always but your calling range doesnt.

Now look at the scenarios.

Villain has 56, which he can have pretty much all isolated combos of, 56ss 87 or 87s 65off. Which is a total of 16 combos. If you jam he always calls and always wins so your loss equals the additainmol amoount. In this very case, it isnt that relevant as you dont shove for much more, but the consideration should be applied to possible deep stacks scenarios in which shoving would make a big difference.

Now villain has QQ or 77, which make 6 combos, some of which will have played the hand differently OTF. Even if he alwys calls with his enitre 6 combos here, compared to the 16 combos of 65, you lose by shoving.

Until ill be shown otherwise by the field im folding

At low stakes you can pretty much fold 100% of your non-nut hands to river check-raises. That's not to say that you never run into a bluff, it's just that essentially nobody will be overbluffing in that spot and you can just fold.

In this particular hand I can't even see how this is a particularly good bluff catcher, so it's an easy fold. (meaning you have no blockers that you want, but you have anti-blockers that you don't want)

Turn is most likely a bet btw.

" At low stakes you can pretty much fold 100% of your non-nut hands to river check-raises" Seen enough weird stuff to dissaprove this statement.

I would call as it would be really strange for him to have 56xx there, especially with that betsizing. At PLO10 some fancy regulars are making some strange bluffs, and here opponent knows that hero doesn't have 56xx EVER. With betting the river he knows he doesn't have that much of folding equity but with c-raise he can give a lot of pressure to hero.

Don't know about you people but im playing 456 the exact same way and im playing all combos of it from the bb vs btn. And i didn't come along with explo folding since from what i see jonna agrees with folding vs river c/r. Also the situation you gave example for has one more street left to play so probably fish is value shoving vs sets. However if you do want to call this you should find a better hand like AQ(5/6)+ I agree that the river sizing should be pot but villain doesn't necessary know that.