Fair enough. I do think there is a popular misunderstanding among the general public about political theory as well as political labels so maybe you shouldn't take that as justification for anything, but I can admit there is gatekeeping and puritanism that happens among the Left in terms of letting people into particular parties/collectives but also in terms of labels in general.

In my opinion, the baseline is that any actual Leftist wants the abolition of Capitalism. If you don't support the abolition of private property as capital, then you are not a Leftist.

Centrists and Democratic Socialists have not been great examples of Leftists to me so I assume anyone who unironically identifies as such is more aligned with the center-Right (i.e., supports the existence of Capitalism but with reforms).