Yes, set out expectations. Given the ages of your children this is easier than it is when they are 4.
The expectation is they can watch Youtube and only the approved videos. The consequences of breaking those rules results in a ban for whatever time you think is right. Any additional back chat results in more time being added to the ban.
How you can phrase it so they understand, give them an equivalent scenario. Their teacher tells them they are doing maths, what would happen if they did something other than they were asked? What would be the consequences in school for arguing back to a teacher?
Why then would it be acceptable at school to accept the rules and not argue and yet expect something different at home? This is what you lay out before you give them access to Youtube, or anything for that matter.
If they start yelling, tell them nice and calmly that isn't how we talk to each other and that you will continue this talk when the use an indoor voice. Model this yourself, no shouting unless someone is in danger. Agree with them, yes it does seem unfair but those are the rules for watching Youtube.
If it continues I would say clearly you are not old enough to have access to Youtube if this is how you choose to behave, emphasis on the word choose, they choose their behaviour, you choose the consequence. Name the behaviour you want to see and also share watching Youtube with them, make it part of a thing you do together. For primary aged children Slow Mo Guys was always a treat in school.
And yes I have been through this, I have two sons who had this sort of reaction with Fortnite, other computer games, tv watching, it is a tale as old as time.
Youtube is an incredible resource, but you have to wade through a lot of crap to get to the good stuff. You can also cast it from your phone to the tv that way you control it.