I have been trying to get a definite answer to this question for a while now, and all i pretty much get is a mixture of yes and no's please help me lol
If you plan on playing Comp.(especially at high ranks), really not at all since the main guns used there completely invalidate that stat within full damage range. In QP, it matters somewhat since there's generally more gun variety, but it's still not very important. And you don't need a whole lot if you want a meaningful amount.
Only in very rare cases. for example, if sturm gets overcharged by a special weapon other than drang and gets the slight damage increase from 91 to 95, it can two tap someone to the head but only if they are at 4 or less resilience. That is literally the only example i can think of besides extremely slight differences in shotgun one hit kill ranges but it is so slight that it is probably irrelevant.
You are much better off speccing out for recovery, it is much more helpful in my experience. I believe my main pvp setup on my hunter has 4 mobility, 3 resilience, and 6 recovery or something to that effect.