No its not a topic about some sort of CrossFit/martial arts hybrid – its all about what your packing at the end of your pins. Normally when you wander into a gym its a good chance that the majority of people in there will be wearing a pair of running shoes or some x-trainers, however things can be a bit different in the CrossFit community.
Many people go for what would by and large be considered not your typical athletic training shoe to train in. I personally have a penchant for Adidas weightlifting shoes with the exception being for running WODs I’ll don a pair of racing flats. Reason being a) they are stylin’ b) I prefer to lift and move in the flat sole and find it more natural than running shoes c) they are nice and comfortable.