Okay, thread about these Mandalorians here. https://twitter.com/noorhal/status/1343315223063748611

Some folks - even myself - have found contradiction on Bo-Katan's words to Boba Fett. Some have even called her "hypocrite" about first saying "Mandalorians are stronger together" and then disrespecting Boba Fett, even sharing the same prejudice as Almec. Well, not exactly.

She had insisting already several times to Din Djarin to join them, even if he is a foundling, a Children of the Watch. So why she does not extend the same invitation to Boba Fett?

The key would be to ask how did we meet Boba Fett?
(Not that cameo in ANH from the SE, or the Holiday Special). He was being hired BY THE EMPIRE.
Yes, the same Empire who had controlled Mandalore and that would either had already been through the Great Purge or about to be.

And she is not the only one having that attitude towards Mandalorians being hired by the Empire. Remember this fella here in S1 E3 "The Sin"? He is giving Din a hard time about it.

And that exchange is pure gold - the back and forth between them shows all the conflict between being a Mandalorian and their specific perspective towards what means to be a Mandalorian. We don't know if Bo-Katan and Boba had crossed paths before and in which conditions.

When she says "you are a disgrace to your armour" it's pretty much pointing the finger on him carrying on dirty stuff for the Empire (as we know he did, several times for Lord Vader).

And yes, Bo-Katan taunts him with the knowledge of Jango and Boba's relationship, and by the way he address her back as Princess, he might know who she is too.

(I would have paid to see that fight, TBH.)
But yeah, it's just snark regarding Boba attitude towards not following the same code of someone wearing a Mandalorian armour would be expected, and not outright contempt against foundlings IMO.