For MBB the process and the likelyhood is no different than for a man but is still far from perfect. Outside MBB, as you guessed, some big steps still need to be taken towards equality.
How easy or difficult it is for women to get jobs in ME?
Off-topic: it's about time it gets a lot damn easier.
To address the point raised on "clients in ME who don't approve female consultants". As a firm wide policy BCG doesn't work for clients that discriminate people. If client would make such a request - even indirectly - BCG pulls out of the account.
The process is the same, however, the project opportunities will be different.
Unfortunately, there are many clients in ME who don't approve female consultants. The situation is changing but slowly.
Still, you'll have a lot of consulting opportunities traveling outside the region as well.