This is not a 2A issue. It's not even (currently) a 1A issue. It's a "culture at a private company" issue.
Alphabet (parent company of YouTube) has no obligation (currently) to allow any given speech on their platform. Section 230 of DMCA gives them wide legal protections.
I say (currently) because a real case could be made that content moderation, removal, and algorithmic promotion combined actively curated the platform, and that as such Alphabet is a publisher. This still wouldn't shake them to the 1A and make them stop treating gun goober like redheaded step children, but it might force them to be more even handed about moderation lest they assume liability for content.
Another solid argument could be made that capricious moderation devalues the stock price, and as a publicly traded company they have a fiduciary duty not to allow feelings to dilute stock price.
Both those arguments would take being willing to tackle a Battalion of lawyers to make though.
But in any case, Breen has no bearing on this at all.