I think sympathy and empathy are actually quite good choices in many contexts, but there’s also like-mindedness, compatibility, and a number of others depending on what you’re going for.
It may be more idiomatic to say that two people are of one mind or on the same page about a particular topic or interest.
Based on what you’re trying to translate, I think identification actually is what you’re looking for. It’s a literal translation of הזדהות, and it can refer to the emotional experience of identifying with someone or something, as well as the mundane meaning of a driver’s license or other form of personal identification. Its use is largely confined to the latter definition, however, so one of the other terms is probably a better fit.