The article is pretty clear how they screwed it up. They allowed players who are apparently anti-LGBTQ+ to promote a message that they do not support inclusivity while the point of the night was to do the exact opposite and encourage everyone, regardless of sexual orientation, to feel safe and welcome at the ballpark.
No one is taking away free speech or their ability to practice their religion. The Rays could have said if you don't support this, then you can sit out. There is a difference between free speech and doing whatever you want. The players are still free to share their feelings on LGBTQ issues. I work at a job that requires helmets. It is a required part of the "uniform" to do the job. Some don't like wearing them. They are free to speak out against it. They can likely do their job just as well without it. But if the boss says it is necessary and they want to work, then they have to wear it or find some place else to work.
As the article said, the organization made the decision to put rainbows on a uniform. Uniforms signify unity and the Rays failed to show unity around this issue. So, yeah, they screwed it up.