I've seen lots of twin robot cells with both earths connected to the same fixture, at times they weld within inches of each other at the same time without any problems.
The OP didn't mention what machines he has and I would assume its a Transformer based mig and a inverter Tig or MMA?
There are definitely issues if it would be two inverter based ACDC Tigs on the same job. You need special software to harmonise the switching. When one is in negative the other is in positive and so on. If not it can cause the inverters to blow with prolonged use.
I have three earths connected to my bench,
One transformer type mig,
One inverter tig,
One inverter plasma,
Also have another separate 3m long earth lead thats bolted to the bench and the nearby chassis jig, that way theres no need to constantly move any of the three earth leads from bench to jig as it's all permanantly earthed.