No. But if you set up your dies with the one brand that the one you must always use. The RCBS may set you cartridge base a few or several thousands higher or lower than the Hornady shell holder. That can really mess you up your shoulder bump if you swap them around.
Hmmmm, I always match the press with the same brand shell holder.
I have come a cropper by using LEE shell holders and RCBS presses, it was an anomaly I'm sure, but still a PITA.
All shell holders for sizing presses, have a height of .125". How this varies is beyond me.
Oddball rim thickness has caught me out also, again with LEE shell holders.