"If we were to agree" vs "If we are to agree"

I suspect the answer is "Neither of them". There are three possible clauses in this situation, and they have subtly different meanings.

If we were to agree, do you think we could start next month? is a remote hypothetical ('I know it's unlikely, but just suppose').

If we are to agree... would normally preface some sort of demand, like ...you will have to start by raising the price. Technically, it's imposing a condition that must be fulfilled before any agreement can be considered. (This condition might, of course, be that 'you agree to start next month', in which case your second example would be correct; but even then it isn't the best way to express it.)

The normal wording in your sentence is just If we agree on this deal, can we start next month?

If we were to agree on this deal, do you think we can start working on it next month?

This means that if you agree on the deal you will be able to start working next month. Agreeing on the deal does not depend on you starting work next month.

If we are to agree on this deal, do you think we can start working on it next month?

This means that making the deal depends on if you can start working on it next month.