The Big 12 branding will be comparatively small and there will be far more BYU. I don't think most people have an issue with a small Big 12 logo showing up on some BYU gear, it is just when the Big 12 logo is the only thing or just as big (or larger) than the BYU logo (like the Utes did) that most here have an issue.
We are BYU fans. We might cheer for the conference but mostly we are supporting our team.