Ok, so, I think the reason the "sex organ" thing is so contentious is because the penis (and the spectre of the mythical transfem rapist) is so tied up with the ways in which we're attacked and discriminated against. A common vector for twerfs to attack us from is that we have the "rape organ" which is so inherently evil and violent that it taints us by association and even its implied presence is de facto violence that marks us as inherently male (twerfs LOVE to conflate maleness with inherent violence).
In addition, tucking is painful and works to constantly remind your brain of the presence of your own penis; generally not what trans women want to do. It should honestly never be expected of them; the correct answer is for everyone else to get over it. There's plenty of places in the world where nudity is much more acceptable; the United States and the UK are anomalous in being incredibly sex-negative cultures.
The swimming thing is also a fraught subject; like gaynessopimizationalgorithm said, that's exactly the place we're most likely to be harassed. There's a very poignant post on Tumblr asking about what trans women would do if, for a single day, cis people didn't exist, and a large chunk of the responses were "go swimming."
In my opinion, the main thing about society that desperately needs to change isn't gender abolition, it's the unbelievable sex-negativity in western culture. Being able to see someone's parts through their clothes is not violence, has never been violence, and will never be violence. In general, it's not a violation of anyone else's consent to dress how you want in public. It's your responsibility as an empathetic human being to not make your discomfort with another person's self-presentation their problem.
This actually provides a good example of what I said last time about why I, personally, don't trust gender abolition as a concept. If you hold this view, that a part of our body is inherently obscene when presented in the same clothes as a woman, then how can I possibly trust you'd treat me the same as a female peer in a genderless society when you're so hung up on my body? We'd just have gender again, but with plausible deniability since it's only about how we present our bodies.
Sorry if this got heated, but again, I hope you take this to heart. I really do believe you want to do right by transfems and are trying to learn, and I want to be able to help with that, though I do unfortunately think you may need to discard the gender abolition if you're serious about wanting to act in our best interests. Think about it, ok?
Okay I’ll think about this.