Nothing is more delicious to conservatives than a small, powerless group who do not fit into the so-called social norms to attack as a scapegoat. Perfect for distracting their supporters from all of the fuckery and wanton neglect that conservative parties pursue, and perfect for whipping up emotional fervour in the mind of those who cling to conservatism out of fear of difference.
Other groups & causes which conservatives tend to target may willing to jettison the needs of a tiny group for their own ends if they can get their own ends met, and fracturing solidarity is incredibly useful, if not essential, to conservative goals.
As such, people who are seeking treatment for gender dysphoria are the perfect target for the GOP to rail against.
If they remain US citizens, they will have to pay US capital gains tax on the sale of their home in the place they now live. They'd also be liable for US federal income tax. This would be on top of whatever taxes they're liable for in the country they moved to.
If they have renounced their citizenship and are no longer resident in the US, then they're (broadly) no longer liable for US taxes, including US capital gains on the sale of their home.
Renouncing citizenship is expensive, but massively cheaper than the taxes they'd pay as non-resident US citizens. I'd assume their income had come in under the threshold or something, so the matter only came up when they wanted to sell their home.