For the second part of your commented you added after I quoted it: there is no "way around" going through NPC recuritment. If you identify as a woman you can participate; if you identify as a man you cannot. I'm honestly not sure what gender non-binary people do but I've heard of them getting bids anecdotally.
Whether a trans woman would get a bid depends on campus culture, chapter policy, and national organization policy, and that's a whole other ball of wax.
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