Telling someone to “learn to live with” abuse is not okay. It does equate to “shut up”. Worse, it equates to “shut up I don’t respect your identity enough to care when you suffer personal abuse”.

why on earth would you think that a parent would be less racist than their child?

Not in the slightest. The winning (and only correct) stance to have here is zero tolerance for conservative racism and sexism, and for Twitter to devote more resources (less profit, more hiring would work) devoted to combatting it instantly, firmly, and loudly.