JFBConnect doesn't have individual settings for importing profile vs importing avatar during login right now. It's something that's planned for a future release though.
If you want to make a very small edit to our code, you should be able to disable the profile import pretty easily. To do so, edit the /libraries/sourcecoast/plugin/socialprofile.php file. Around line 125, you'll see:
$this->importSocialProfile(); // This will import fields from the user's profile
Simply comment that line out by adding // to the beginning of the line.
Test during registration and login and see if that does what you're looking for. Also, please note that you'll need to make that change again any time you upgrade until we break those settings up further.
Thanks,
Alex