IMHO, you need either All Mail (and nothing else), or everything else except All Mail.

Gmail stores all the messages in All Mail and labels them. They are presented as if in folders by filtering on labels.

Personally ,I don't want or need to be aware that Gmail does things in this idiosyncratic way. So I don't subscribe to All Mail and work as if it was all just based on folders like all my other email accounts. But if you're just "backing up" an account (why? Gmail are rather less likely to have a catastrophic data loss than the average home user) the All Mail folder should serve you well, since presumably you're not intending to actually use this as a working account on Thunderbird.

If you're worried about the security issues of leaving messages on someone else's server, maybe you shouldn't be using Gmail.

As I also said, I want a portable backup for offline use etc. And I also need the labels. If I unsubscribe All Mail I would need to have labels for all emails in order to have all of them, since unlabeled ones would not be synced. Additionally I need it for threaded conversations with different labels.

Anyway, since it should be supported there's no reason to find workarounds but it should work and that's why I want it. If it were not supported I would just have to deal with it,but It is, so any actual suggestion?

If I unsubscribe All Mail I would need to have labels for all emails in order to have all of them,

That's the whole point when you want to use Thunderbird to backup your Gmail.

since unlabeled ones would not be synced.

Can you explain that in more detail? You were complaining about messages being downloaded twice. Zenos explained how to avoid that. https://support.mozilla.org/en-US/questions/1117013#answer-863081

Now you complain about messages not being synced? You control what's being synced in your Thunderbird Synchronization settings.

So, I have labeled emails, right? which appear as folders. Beside the emails with labels, there are also emails that don't get a label, e.g. they come in the inbox, and I just archive them directly, so not all emails have a label. Even if I had a label for every email, I would also like to have All Mail for seeing threaded emails where one thread has emails with different labels. I hope that's clear. Still, Thunderbird's documentation says it should support Gmail labels, so you guys are still not explaining why it's not working and how to fix it. There are many reasons why I might have emails with multiple labels, beside All Mail, and they still download double. That is the problem here.

There are many reasons why I might have emails with multiple labels, beside All Mail, and they still download double.

As per https://support.mozilla.org/en-US/kb/thunderbird-and-gmail that shouldn't be the case. I still don't see a point syncing 'All Mail' though.

I have the portable version

The portable version isn't a Mozilla product. Contact PortableApps for support of their product. If the double download also happens with the Mozilla version of Thunderbird please open a bug. https://bugzilla.mozilla.org/

Beside the emails with labels, there are also emails that don't get a label, e.g. they come in the inbox, and I just archive them directly, so not all emails have a label.

In which way is that a problem?

I would also like to have All Mail for seeing threaded emails where one thread has emails with different labels.

You can use 'Open Message in Conversation'. 'All Mail' is not needed for this.

Like I said, emails that don't have a label can only be accessed through All Mail, and if I don't sync that, I can't read those emails. And since it is downloading twice for me, although as I said, and you also posted the link, it should download only once. That's why I'm asking if I'm doing something wrong or why is it happening? It happened on the install version too.

EDIT: maybe the configurations in the Config Editor, could any of them cause this?

It happened on the install version too.

Please let us know the bug ID when you raise a bug in Bugzilla.