Trigger warning: explaining jokes in way too much detail.
The phrasing is a reference to the "Is this a pigeon?" meme (see: https://knowyourmeme.com/memes/is-this-a-pigeon ). This is meant to indicate that this is clearly not egg_irl, but the topic of the original post seemed like something repressed trans people can relate to in hindsight. It reminded me of a common pattern among eggs where there's a vague but insistent internal voice (not literally a voice, more like an occasional impulse) telling you to do things that you associate with your actual gender, rather than your assigned gender, with varying effects depending on the person. For example, it generally made me feel uncomfortable without understanding why, leading me to assume I simply didn't like those things, when in fact that was more or less the opposite of the truth.
Anyway, these sorts of things can make the idea of an unknown, voiceless, internal personality separate from your surface-level persona resonate with trans people. Add the fact that when you're deeply involved in gender issues and transitioning, it's so much on your mind that there's a tendency to interpret everything as being somehow related to gender even when it isn't, and it seemed like a good fit for the pigeon meme.
As someone who realized they are trans and therefore also gay within the past year...