Problem 1 - who decides what's wrong? ...
What if the 'strong belief' was that they should wear a patch calling for all black people being made slaves? You can say, 'oh that's obviously offensive, a straw man', but wait. Who's to say that? What if that's how they feel and they think it's a principled stand?
What if the team wears pink ribbons to support breast cancer research, and someone has a principled objection? Maybe they think women are too uppity and should be subservient and not given that attention. Maybe they think men aren't getting equal treatment. Whatever.
The point is, because it all comes down to 'opinion', and what seems obviously wrong to one person can seem right to another, there are going to be differences of opinion.
And the bottom line is that to settle this, someone does say 'that's right'. Hopefully they don't abuse the power, but that's something that happens. And a position in favor of equality, welcoming a group who has historically faced discrimination, has a good case to be the 'right' side.
Whose to decide right and wrong? Depends on the meaning of "deciding" and in what context decisions are made. Certainly every individual is capable of making a judgement of right and wrong, but if you mean a judgement can be based on nothing more than a question subjective opinion, a "gut feeling" then I think that is in error.
All the questions you raised comes down to whether or not a person is willing and capable of basing their judgements on a morally derived principle and if they are willing to apply such principles neutrally to all. For example:
- Jack says government may not prohibit the religious practice of Christians. Why? Because, he says, the Christians the best folk, unlike Muslims.
- Jill says government may not prohibit the religious practice of anyone. Why? Because all people have a right express their conscious.
Jack's judgement is not based on a neutral moral principle and its neutral application, and its so narrow an application that its not a principle.
However, Jill's judgement is based on a higher principle and application , and is neutrally applied to all regardless of whether or not she thinks they are 'the best folk'.
Much the moralistic banter in this thread is mostly by the "Jacks" of the world, people who say "X is right because I say so" or "because I like X". And sometimes the "Jacks" are not always aware of it, couching their "gut feelings" in undefined sentimentalities that pose as saying something.
For example, if Jack says
"And as for a position in favor of fraternity, welcoming individuals that have been mistreated supporting fraternal relations, is a good case to be on the right side".
The reader wonders. What does he mean in the word 'fraternity'? How is it defined? Exactly what neutral principle and neutral application is Jack advancing? Is it that only those who advance fraternity (whatever that is) should be welcome? Or that only those who have been mistreated due to their support of fraternity should be welcome? Why not others?
Anyway, the proper resolution of many of the disputes in this thread revolve around finding a robust moral principle(s) and applying them neutrally. To that end the reader should state what issues they see in this story, and find moral principles neutrally applied to all.
If, for example, a person says its okay to refuse to wear "negros should be slaves" but not "gay pride logos"...why based on what principle?
If, for example, the coach says everyone has to wear an evangelical T-Shirt, is that okay...just as gay pride logos are okay? If not, why not?
If, for example, the coach says to wear pink ribbons, is it or is it not okay to decline?
Find the moral principles in play, define them, and apply them neutrally. Therein you shall find objective moral judgement.