"They" have chosen to voice their protests in this manner. What I think "they" should do differently is of no concern. We all choose to agree or protest in our own fashion, and that is another Right enumerated within the Constitution.
Yes and no.
Yes ... they are free to protest whatever false narrative du jour they choose. As long as it is peaceful. Don't break other people's property. Don't cause a drain on LEO resources that could effect others. Don't block roads. No one has a problem with peaceful protests.
People don't like this and find it a sign of disrespect? That is their right too. They can choose not to watch whatever it is. Let the market decide.
No ... if their employer or league tells them "no" while they are on their employer's dime, then "no" it is. They do not have a right to protest in the course of their employment if their employer/league forbids it.