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I think critiques of Catelyn's attitude towards Jon aren't an indictment of her as a character, but of the attitudes the prevail in Westerosi society at large. Part of what makes Cat great is her deep understanding of Westerosi politics and societal norms and her deftness at all
primogeniture exists to prop up this system of accumulation of weath and power for your own tribe. Bastard born children are a threat to this system and therefore society has perpetuated myths about the inherent moral inferiority and duplicitous nature of bastards in order to
weaken their societal positions and prevent them from obtaining power and staking a claim that would jeopardize the "true" family. But we see time and time again that this ostracization leads to self-loathing and a deep need for bastards to prove themselves to be "better" than
their bastard blood and the equals of trueborn children. Then you get characters like Bittersteel, Bloodraven, and Daemon Blackfyre who all have this chip on their shoulder because of their bastard status and legitimizaton doesn't undo those years of an enforced inferiority
complex and it reinforces the prevailing view of bastards as grasping, greedy, and inherently traitorous which Westerosi society responds to by casting them down all the harder and trying to ensure that they can never rise from the muck to overthrow their trueborn kin.
