I don't think he needs to do anything to force it! 50-50 he's traded anyway. But I also don't think this would be a big enough deal. If anything, the message he would have received this year is that the Phillies have no problem with it, and some of his best teammates have his back.
Also, while I don't agree with what he shared, it's not like it was outright misinformation or propaganda. Heck, being against vaccine mandates and not thinking you should you lose your job because of it is technically the official position of MLBPA.