That particular quote - in fact, that whole scene - still gets used by myself and people I know. It mainly serves as a shorthand for "I don't have time to explain why, but doing what you're about to do would have catastrophic results."
There is, however, a secondary use of "don't cross the streams." There are situations where you have, basically, a good thing over here, and a good thing over there, but if you try to bring them together, well... "It would be bad." This can refer to foods, or friendships, or social circles, or genres of writing, or just about anything else - but again, the quote is a convenient shorthand.
Do you have any quotes that you use like that?