I have now tried extensively to find any possible other process that might be updating Thunderbird. I could not find any. However, right before Thunderbird updates itself, I can find a crash log in the console (but I do not understand its content).

@Wayne Mery and @Mapenzi : do you have any idea how I could fix this problem which looks like coming directly from Thunderbird?

We'd have to see the error you mention.

Ok, I tried some more around and might have found a stable solution. I completely deleted the folder with all Thunderbird provile information (the folder user/Library/Thunderbird) before reinstallation. So far it has not upgraded in 2 days.

(I now have other issues, like freezing upon opening and not being able to open attached files, but for that I might find a solution somewhere else).

Ok, it was false hope. It update again after 3 days.

Dear all, it in the end was indeed that there is JAMF program installed on my MAC which had the channel set to "release". Frankly, this is very confusing why the release channel would direct one to the beta non-release version. But, after now setting it to ESR-release the problem should be solved. Thanks for the patience and guidance with the problem.