I had the same problem. I've found that you can continue to log in to both but it's a little tricky. You can only login to one at a time (regardless of the starting point). So if you login to your Marriott account and then go to the SPG site it will show you only your Marriott account. Same the other way, if you start on the SPG site and log in it will log you into your SPG account.

If you choose "Remember me" when you login (the default) it will stick with that account, regardless of sign out. To switch you need to sign out, and then at the login page click "Clear Remembered User" and then login from the appropriate side for the account you want.

I've been using an incognito tab in chrome so I can login to both (you should be able to use private browsing in Firefox or IE for the same affect).