Is there a way to abandon quests? I have zero interest in the brawling quests. They take up a big chunk of my journal, I would like to get rid of them from my journal to organize it.

Any ideas?

In your journal (J key) just select another quest and your active one will be changed.

Same. Although you get a cool ride from one of them.

You could try to complete them. Get gorilla arms, lower the difficulty to Easy, go through them and just spam the left mouse button. On easy you don't need any tactics. Only the last one cannot be completed with mindless spamming on Easy mode. But if I remember right you get offered to take a dive in the last fight and receive a lot of eddies. So basically, you don't even need to fight in that last fight. You won't get street cred if you take a dive, but street cred is easy to come by.

There's also a method of getting a melee weapon smuggled into the ring, but gorilla arms and easy mode is enough that you don't need any tricks.

You can set the difficulty back to whatever you play on after completing this. I begrudgingly completed it with a Netrunner build where I specced all into INT and almost nothing in strength, but still, setting Easy lets you to "bypass" all the fights except the last one with just spamming.

I also did that just to get those quests away from the Journal. Not a big fan of boxing games.