Hi Vytautas - thanks for you question. I am not having the same experience. I just did some testing with a separate test account, and the Personal Email field was enabled. I was able to add a separate email value, then save my changes with no issues.
This is the path I followed: Logged in>Edit Profile (in drop down by avatar)>add personal email in Personal Email field>Finished.
Please include an image of what you are seeing if different than above.
Thanks for clarifying. Since we have single sign on (SSO) going between 2 systems (the Community members directory and our Support Center registrations) checking based on email occurs between them. They need to be in synch when you log in, otherwise an SSO error is displayed. These cases typically occur when a member's work email changes. Because of this, I need to make the change on the administrative side (and why individual users aren't allowed to change their email).
In your case, since you want to use your personal email, let's try my normal process for changing email and see if it works. Just be aware that you won't be able to log in with your Support Center credentials, but will need to use the new personal credentials. If it doesn't, you may have to create a new community registration with your personal email.
I will send you a private message with my email. You can send the email you would like to use for your community account. Thanks.
Vytautus - A couple of weeks back I sent you an email with some further info, and followed up again today. If you would like to proceed further, please let me know.