Perhaps the solution is to have two e-mail accounts: a GMail account to communicate with GMail users, and a non-GMail account to communicate with non-GMail user

Perhaps the solution is to have two e-mail accounts: a GMail account to communicate with GMail users, and a non-GMail account to communicate with non-GMail users. Ideally, also a client that handles all this automatically, i.e. chooses the right sender account depending on the recipient, so that I don't have to think about it. Just like Pidgin was a common solution for AIM and ICQ, this would be a common solution for e-mail and GMail.