I notice that Haley claims Mulvaney's gender presentation "mocks women." That's odd, given that Mulvaney is fairly traditional about her dress and makeup. She's not a drag queen. Perhaps Haley is mixing up her messages, because "mocking women" is something the right often say to disparage drag queens. Given that Mulvaney does not in fact use parody the way drag queens do, the only takeaway is that Haley believes trans women mock cis women merely by existing -- that trans women should not exist.
Well, it's not the only takeaway. She's a politician, after all, and politicians of all persuasions have only loose relationships with truthfulness. Mulvaney might just be saying what she's saying because she believes (or advisors have counseled her) that her slurs will advantage her with conservative voters.
Either way, she's attacking marginalized people with nonsense, and she needs to stop.