I have heard that it is anti semetic to "deny israel has a right to exist"
Which makes me curious. Is it a generally accepted premise either in law or just by people that countries have "rights"?
I think of rights as something people have.
If countries do have rights, is exisiting one of them?
In international law, yes. At least in theory. Powerful states can usually do what they want to less powerful states, but the international order supposedly guarantees a recognised state's sovereignty, certain rights of trade and passage through waters, and a number of others.