They both know this stuff helps their brand.
It could've so easily be avoided. How many golfers on the PGA Tour do you think don't get along with Patrick Reed?
This doesn't even seem to be a substantive beef. Did anything happen other than they find each other annoying? Even if Bryson said something to Brooks in the background of that interview, it's not like pro athletes don't rib each other. Why should that carry over as a substantive disagreement?
They both dislike each other and their personalities class, but this seems 100% petty and performance art.