The cost of a haircut depends on where you go. There are plenty of places where a haircut costs the same for men and for women. If you go somewhere more expensive, it's going to cost more. Also, more women than men have long hair, and more women than men color their hair. Every average person knows all of those things, so the first part of that answer is a tactical mistake.
I haven't read much about the "pink tax" or talked to men about what they pay for beautifiers, but I also think it's a mistake to answer the criticisms by turning the controversy into a discussion about the type of gender discrimination that's "morally wrong and threatens economic insecurity." Someone who can pay $300 for a haircut is not struggling with economic insecurity.
The controversy is based on gender discrimination, but it is based on gender discrimination against women in power rather than on women in general, and it's important to keep that in mind. When Representative Ocasio-Cortez was elected, it made her different from the average woman. She can remember what it's like to be the average woman, she can have concerns for that experience, and she can fight for regular people, but to defend herself against unfair attacks she has to recognize her new status.
This is an unfamiliar situation because not many young women are elected to Congress. I would address it by trying to think of parallels, rather than differences, between myself and my male colleagues. Since there isn't a direct parallel that's going to be comparable, I would ask information-seeking, rather than accusatory, questions such as "How much does the average male Representative or Senator spend on a suit?"
I might also talk about the seemingly never-ending misogyny of ridiculing women for not "taking care of themselves" while also attacking them for vanity. I think that speaks more to the heart of the issue. If I were going to try to be funny about it, I might take a picture of myself wearing an ugly outfit and with my hair looking really bad, carrying a briefcase and on my way to work. I would Tweet it with the caption "Would Americans rather I represent them looking like this?"
Standard highlights cost around $100. $300 is not a crazy amount of money; a lot of people pay that much for their hair. Some grumbling might have been reasonable starting at around $500, and $1,000 definitely, but that's not what she did. Maybe also try publishing some statistics about what haircuts cost; keep it factual.
She's not known for outrageous style decisions. She dresses conservatively and appropriately. She's not buying expensive jewelry, as far as I know. How much does the average Congressman pay for a watch? Cufflinks? A tie? Lunch?