I wonder how your national classifications compare to EN European or BS British standards? Under either of these the colour of the adhesive is irrelevant.
I wouldn't have thought white over grey matters from an adhesion point of view. I think it's less common and more expensive because of extra processes. But I wouldn't have thought those processes to remove and / or add colour change adhesion processes.
In my country I heard this from some people in related industry. They said that white tile adhesive is made by white portland cement. And white portland cement strength is weaker than normal(grey) one. I am not sure if this is true.
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Not sure what adhesive you are using, but most here have a TDS that states bond strength, sheer strength and all other performance properties. I have never noticed there to be a difference due to color.
No difference between white and grey in terms of bond strength when directly compared under EN standards. There may be some brands that differ from others and some dont conform to EN standards which may be weaker or stronger.