In certain spots, based on your holding, your opponent's perceived ranges, stack sizes, pot odds, etc. would it ever be possible that, in response to an opponent's bet or raise, a fold, call, and all-in shove would all have the same mathematical expectation in the long run?

Folding is 0EV, so you'd have to create a situation where shoving and calling also work out to neutral expectation.

That's not exaaaactly accurate, but I suspect it will steer you in the right direction.

Sure you can . As Gonso said you need to have all 3 be 0. So you need to find a situation that all in has 0 EV (or at least nearly 0 since its never a perfect guess just an estimation given ranges you can never perfectly define). Then you need to create a pot and a stack and a bet size that will make the call an inevitable all in on the next betting round nomatter what cards comes due to pot odds etc . Then you will have both equal since the call becomes an all in anyway. Then you need to find a situation where the opponent will see your all in as also an inevitable call on both occasions so you have no extra fold equity. That would be one solution.

Example; Say you are in a tournament situation an you have a trashy hand like 103o with only 8bb left. You are in the big blind. The antes add up to say 0.75bb . All fold and its down to you and the small blind who is a typical bully with 50bb raises to 6bb.
Your range vs this guy that is likely on a random or maybe top 96% hand (say he folds stupid hands like 23, 72 etc) (in fact proper theory i have posted about in the past indicates that as long as you are below 10bb and he has big stack he must put you all in with anything and its plus EV for him anyway) . Against a 96% hand (say he folds all the stupid low 4% ones as 72,62,42,32-off) then your 103o is 41.76% as all in.
Its important that you do know the guy is a blind stealing sob bully (ok after my theory re push above i can no longer view all those guys as sobs but its ok lets call them that for fun since one has to always feel pissed off when forced to push with 103off anyway) . That 41.76% (ie hand 103o)is carefully selected to be such that it gives you an average final position if you push of 7bb (8+8+0.75=16.75 as this times 0.4176 is about 7bb) .

Now you can fold and end up with 7bb. If you only call you pay extra 5bb and have 2bb left and it doesnt matter what flop you get you still put the other 2bb at the flop because he will bet anyway and you cant fold with 2bb left only on a 12.75bb+4bb pot when he bets 2bb at flop). So there you have it both call and all in end up as all ins anyway by the river because the guy simply will not check it all the way down leaving you 2bb. They never do that lol! Therefore both options equal to all in and as all in the average final position as we saw is 7bb.
So all choices are basically 0 EV or at least nearly identical since you can never have perfect range information but given the details of proper play you have to assume the guy is on the range i gave above especially if you have seen him being loose bully like that for many other prior bets.

There you have it then . Big blind with 8bb stack having T3 off and sb raises to 6bb. Lets even assume we are so far from bubble that no other pay structure considerations matter and tournament equity is almost nearly identical to cash game equity for the given situation. Or identically you can assume its a cash game that you just lost a big pot and didnt have enough time to reload to 100bb as you found yourself in that position.

Anyway you can build any such situations by selecting the stack x you have to be such that (x-1)/(2*x+0.75)=equity vs his range for the hand you have and adjusting his raise to be say as big and even better a bit more than half your stack. This forces you all in at flop anyway nomatter what happens so call = all in eventually so why not do it in advance anyway and push. Push=call=fold= (x-1) bb.