ATS won’t fit my two new front tyres on A5 Quattro

I have heard this for our BMW Xdrive system from the service department, but they didn't say not to do it he just said the oil in the transfer case will need to be changed sooner due to it wearing quicker, but totally normal and the computer tells you when to change the transfer case oil.
Yes its not ideal to have the front wheels turning at a different speed in a straight line to the rear but the centre diff should surly handle this in an Audi

Yup. DuckDuckGo 4 wheel drive transmission wind up. Always try to keep both ours (both 4-wheel drive) within 3mm.

Whether the A5 suffers from it, but that is why they are saying no...

I've always made sure that I've moved the wheels front to back frequently to even up wear for this very reason, I know that my old VX Cav GSI 2000 4X4 would show its annoyance if I tried that trick on it, these cars disabled the drive to the rear wheels during braking and you would feel/hear a big rubbery bump that told you things were not as they should be - that was only due to me buy 2 new tyres each from 2 different outlets to save money, I was a bit annoyed with Pirelli over that, sorted that out by buying yet another 2 tyres!
While owning a 2000 VW Passat 4Motion, I always equalised the wear by moving the wheels front/back some with B8 S4, it just makes sense though Audi don't seem to have written anything in the S4 manual that suggests you should do that.

I'd say 10/10 for ATS for working that way with any 4X4 as normally the customer knows nothing and will do nothing until it goes wrong, though I would have thought they could have offered to get you to sign a disclaimer, though maybe not the way they work, just easier to say "no".

Edit:- when I replaced all the summer tyres on my S4, I chanced on an extremely good deal via the AA, it beat every other online supplier - and they sent me to ATS who slightly nipped every wheel with their kit, a bit annoying at first!