Actually I don’t know why this is happening yet.
I suspected that you were connecting to Youtube initially on one WAN and then the traffic was being load balanced and so youtube gets confused as it sees you requesting from two public IPs at the same time and doesn’t know where to send the traffic. That’s why you need a https persistence rule that looks like this:
Easiest way to test that is to create an outbound policy set to enforce for a PC connected to the LAN so that all of its traffic uses a single WAN eg:
Then check that youtube works. If it doesn’t work using a single WAN then something else is going on.