The answer to your question is exactly analogous to asking "who has the gift of healing?". We know that it is not everyone.

We only have one story of survival of snakes/poison, and it is significant that it is accidental. Paul did not say "I'm telling you the truth, and to prove it I'll pick up this deadly snake". He picked it up by accident, and God used that.

So the likely answer is that God gives the gift of poison immunity to people who need it because they have involuntarily taken poison and who he wants to survive it.