Not sure if its worth going to war over either. I"m a guy that doesn't make waves but if I'm accused of something that I feel I"m not wrong on or didn't do I'll go down with a huge fight. Don't think this is the case but your call
Not sure how expensive or if this is your fav jacket but you could just simply remove the cross.
Stitch removal tool so you don't damage the material. Might leave the holes behind but over time the threads will swell with moisture and close up.