Not all contracts are valid.

This is not an answer. Invalid contracts are usually invalid for a specific reason.

I really was only answering the bit stating;

>"You sign a contract that you won’t do it."

As that is not the be all and end all of contracts.

Yeah but why in particular wouldn't this one be? There's no reason you couldn't have it be a condition of a contract that software licensed under some particular license isn't allowed. Choice of software license isn't a protected class or anything like that.

Doctrine of equality does not apply to private trade of products and services. This is not a public procurement announcement and they can disallow particular products to be used in their premises.