I just called and asked this question. After asking them 'why they discriminate against bully breeds,' I was told that was their policy. Discrimination at it's finest.
I'd setup a visit to the facility. I have a boxer who has been going there since she was older I think. I also know someone with a pit mix that was turned away for that reason. I think it's worth you taking your pup in to see them to be sure.
My dog is a pit mix who is three and she has been going to You Dog's Best Friend for years without issue
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