Every camera will reproduce colours a certain way because of the sensor used, and the way the files are processed in camera, both RAW and Jpeg. I know in the past that Nikon camera used to easily over saturate the reds in comparison to other brands. I don't think that is the case anymore.
Where cameras have the same sensor, they may reproduce very similar colours, if not the same colours, but engineers will no doubt fiddle slightly between models which may affect the colours. So all the Canon APS-C cameras which use the 18mp sensors (and there are many

) will probably give similar colour reproduction. The Canon FF cameras may give slightly different colours to APS-C cameras, but also to the different FF cameras. One would assume that Canon engineers try to have all their cameras reproduce colours in a similar way. Other manufacturers will do things in a similar way. All the Nikon DX cameras using the current 24mp sensor may reproduce colours in a similar way.
Of course that is if the same Picture Style/Control is used for Jpegs.
You can match the colours from two different cameras exactly by using Lightroom and a Colorchecker Passport.
That has been my experience anyway, but I think you may have two different Canon cameras Kipax from some of the threads I've read here, so you could take a picture of a scene with as many colours as possible to see if that is actually the case. :shrug:
For the original post, I can see logic of Wedding Photographers preferring people with the same brand of camera gear, for the colour reason I mentioned above, but also for compatibility of lenses, flashes and accessories. Having matching could cut down on the amount of gear that needs to by carried/taken to the wedding.
Also, if things were to go really wrong, and all the main photographers gear breaks, gets stolen or some other catastrophe happens, having a familiarity with the 2nd shooters gear would be beneficial.