If their descriptions about the nature of their gods are different enough, it is insulting to both to claim they are worshipping the same one.

So far as I'm aware neither Mohammed nor his followers have ever for a moment suggested that Allah is "not the same" deity as worshipped by Jews or Christians. To suggest anything like that would in fact be inconsistent with the reiterated profession that "there is only one God".

Essentially these are variations on the same religion, especially Judaism and Islam. All three have holy books and all kinds of other things in common. Including at times some things that aren't too nice.