In UK, it is an impolite way of describing something that someone is doing to make me angry, even if that thing is trivial. “don’t f………” = back off – do not interfere with what I am doing, if you do then you will regret it.

It's an expression used when you're doubting what a person is saying (with intense emotion like, for example, you're angry ^^) Take this situation for example, if you have a boyfriend and a friend of yours says that your boyfriend is cheating on you, a normal reaction from you would be "Are you kidding me?" or "You've got to be lying." or "Don't say such things!!" or "Don't lie to me." In this case, "Don't fuck with me" can be used (in a vulgar/impolite way ---- but i do not recommend it ^^) as another way of saying "Don't say such things!" or "Don't lie to me" as mentioned above.^^

very flexible spoken saying, could be that meaning depending on the context.