I really thought I was asking a question to Mozilla Support, because I choose 'contact us'. This is very misleading because that header gives no contact information whatsoever. Now I see my question on some forum, and my email address is accessible to everyone.

Firefox and Thunderbird are fine products, but this situation does not make me happy.

The donate page has a frequently asked questions link

Which explains that

Why do you need my address in order to process a gift? We understand that your privacy is very important. We ask for a minimum amount of information required to process credit card payments, including billing addresses. This allows our payment processor to verify your identity, process your payment, and prevent fraudulent charges to your credit card. We keep your information private — if you have questions, please refer to our Privacy Policy. If you would rather not fill in your information on our online form, you can mail us a check.

The donate page also has a contact us link which takes you to this page which will get you in touch with donor care where you can ask your question of people who actually know how the system works, I really only know Thunderbird. I have no personal experience with the donation process as I have never made a financial donation to the project, I figure my time in this forum is more than enough.

The header with the "get help" on it that I assume you clicked to get here is not shown on any of the donate pages as far as I know. The processing and "donor care" is provided by the Mozilla foundation and as such is not part of the Thunderbird project. (Even though the money comes back to the project and the project pays for the service on a cost recovery basis)

I really thought I was asking a question to Mozilla Support,

You did, that is the forum where the post landed. You even got into the Thunderbird part of it.

Now I see my question on some forum, and my email address is accessible to everyone.

Neither Firefox or Thunderbird have paid support staff, only volunteers providing peer support at support.mozilla.org.

What I can tell you is your email address is not available to all. It is not even available to me as the moderator. I can disable your account. I can even mark all you posts as spam in the process. I can delete your individual postings. What I can not access is your email address. But then I can't access my own either.

Have a look at your profile on this site. https://support.mozilla.org/en-US/user/GVPRAAG that ios what is available. The authentication as a user is managed using Firefox accounts and honestly I don't really know even how the forum knows where to send reply emails. But I assume it asks the Firefox accounts server at some point, just as it asks that server to validate the user name and password entered when you sign into the site.