F12: Thunderbird account creation problems

[Daniel Thurman]

I noticed that Thunderbird has added the "smart" feature
that gets "too smart" by not allowing one to add accounts
for two different servers, serving DNS and Email, and with
the same user accounts.

For example, let's say that you have MX records:
mail1.domain.com (a Windows email system/server)
mail2.domain.com (a Linux email system/server)

Attempts to add or modify one or the other accounts
results in both accounts being changed, "on the fly".

How is it possible to add these accounts?