In theory "impossibility" is a defense to most crimes.
In practice you usually get screwed in one of the following ways: a) the law makes it impossible to do X without breaking the law, even though X is a normal thing and neither law was supposed to be a total ban on X, but you could comply by not doing X at all, b) the inconsistent laws are imposed by different jurisdictions and then they each insist you follow theirs, often a special case of the first one where X is "be in two different jurisdictions" but sometimes the even stupider one where a jurisdiction demands that you follow its laws even when you're not in it, c) it's impossible for you to follow both laws at once so you followed only one of them and then they decide after the fact that you should have followed only the other one.
Do you have some examples of an "X" activity or behavior? I understand the logic you're discussing, but can you help ground it?
Re: imposed by different jurisdictions. I don't know the letter of the law in the US, but here in Australia at least, most such differences are easily resolved by section 109 of our constitution (note: Commonwealth == Federal):
"When a law of a State is inconsistent with a law of the Commonwealth, the latter shall prevail, and the former shall, to the extent of the inconsistency, be invalid."
Hmmm, just googled, and it would seem that Article VI Clause 2 of the US constitution, aka the Supremacy Clause, is basically equivalent.