How to use @mac.com email address with 3rd party mail client

Thanks for asking, but there may be a misunderstanding. I'm not a native english speaker/writer, sorry. What I wanted to say is, that I don't like to enable Two-factor authentication on my @mac.com-Apple ID, mainly because I don't want to use any iCloud-services. Of course I know that Email is a kind of 'cloud'-service too, but it is still different to contact sharing or photo sharing. I have different Apple IDs for App store etc., so it's not this important to have an extra level of 'security' for my Email-Apple ID.

But maybe I'll give it a try, if we can clarify one thing: the document Apple ID - Using app-specific passwords says "To generate and use app-specific passwords, your Apple ID must be protected with two-factor authentication."

Does this mean, I can only use an app-specific password on the mac where it was generated and only with my Apple ID active in system preferences/iCloud?

Or can I generate app-specific passwords, e.g. for Thunderbird, on a one time authenticated mac and then transfer and use these passwords on different macs with no or different Appstore-Apple IDs?

The reason is, that I want to check my @mac.com-Emails on various macs, like it was possible until June '17, without having an Apple ID active in system preferences/iCloud. So is it possible to generate app-specific passwords on one system and transfer and use it on another?

Many thanks in advance for your time to answer!

Thank you very much, Eric, for your fast and extensive response! I've been through all the infos, but I must say, that neither the Two-factor authentication nor the Two Step Verification solves my problem!

Since a long time I used a different approach to get a little security: my @mac.com address was always only used as an Email-Account, like it was introduced about 15-20 years ago. When the Apple ID scheme was introduced, I set up a new one for the App store and a third one for other reasons, all with different passwords. So if somebody steal my @mac.com-Apple ID password, he could only read my emails, but has no contact to the store, iCloud or whatever.

But my @mac.com-Apple ID would by much more valuable, for Apple and who else is listening, if it is tied to all of my Macs and a phone with SMS-capabilities! This is data gathering! I don't see any "security" here.

For people living in the cloud, sharing contacts, photos and music, with iPhone, iPad and a mac, Apple ID-Two-factor authentication makes sense, eventually. But for me it's an Email-Address, which I'm not able to use anymore and I feel Apple is kicking me out...