“Do other gyms find it offensive when a new guy wears patches from another gym on their gi when they start training
at a new gym or cross training at a new place?”
Jiu-jitsu Times: Only if you are wearing a camouflage kimono with patches of flaming skulls biting knives!
Just kidding.
Some more traditional minded schools prefer that you wear a plain white kimono to the classes.
For example, at Gracie Barra the students wear the Gracie Barra kimono, but visitors are okay if they wear a plain white gi.
Many bjj guys say that they have at least one plain white kimono to use when they travel or train at other schools.
So if you are concerned about any possible breach of bjj etiquette, just purchase a basic plain white gi for these training visits.
Generally I would say that the bjj culture is an informal bunch of people and most don’t put very much emphasis on what patches your kimono has.
A personal story about when I made SURE to wear a plain white kimono!
I did a training trip to Rio de Janeiro, Brazil a few years ago.
My first 5 years of bjj were under the Carlson Gracie Team and had always dreamed of stepping on the mats at the famous Carlson Gracie Academy in Copacabana.
I had relocated to a different city in Canada and was now training at Gracie Barra school.
I considered that in Brazil, they can be “old school” and defend their mat against guys from other teams. I had heard stories of guys going to Brazilian gyms and getting really worked.
Would my Gracie Barra patch simulate a big red bulls eye to the black belts in the Carlson Academy?!?
Would the beasts in the academy sit on the side of their mat licking their lips to get a chance to roll up a guy who dared wear another teams colors on their mat?
I wasn’t going to test the theory and got myself a plain white kimono to avoid becoming a possible target.
As it turned out all of the guys were very tough but VERY friendly to the visiting gringo.
I think you are fine to wear your kimono with team poaches to another school.
If you want an excuse to buy yet another kimono, here is your excuse 
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