Conflicting COnditions

Since you used the example, "I don’t care what you believe, as long as your beliefs don’t harm others." I am wondering if that would apply to something many people say "I don't care what you do as long as you aren't hurting others" or in general anything you do is fine as long as it doesn't hurt anybody. Your thouhgts?

"I don’t care what you believe, as long as your beliefs don’t harm others."

Although contradictory, it is not overtly deceptive. The problem is more rhetorical than fallacious.

For instance, if the statement was rephrased as, "I only care about your beliefs if those beliefs are harmful to others", it would be perfectly valid.

Logically speaking, when the implications of condition A make condition B impossible, you have the fallacy contradictio in adjecto, or conflicting conditions.

"I don't care what you believe" implies that what person Y believes is irrelevant to person X. However, adding "as long as your beliefs don't harm others" implies that at some hypothetical point, person X will care what person Y believes - hence, it isn't irrelevant.

The same would go for your example.

Practically speaking, though, anyone in person X's position is simply trying to say that their tolerance for difference of belief ends at active harm, in other words, their patience, like everyone else's, has a cutoff point. Thus, it is really not worth it to call 'fallacy' on someone, especially since tolerance lies on a spectrum.

Remember the exception to this rule: "When the self-contradictory statement is not put forth as an argument, but rather as an ironic statement, perhaps with the intent to convey some kind of deeper truth or meaning, but not necessarily to be taken literally, then this fallacy is not committed."

False Equivalence

self-sealing argument?

The second statement is a separate argument to the first, so it becomes impossible to argue that your beliefs don't harm others without refuting the first statement, which is a statement of a subjective nature that you cannot refute evidentially.  

This looks like a discussion of the Non-Aggression Princple. My experience is it evokes emotions that destroy the discussion. In the 3,000 years of NAP debate, each side seems to have dug in its heels. It is a moral issue, not a logical issue.