It's never made much sense that the entire multi-species Federation would be subject to a strict ban on genetic engineering due to events on Earth that happened centuries before the Federation was even founded. The way they doubled down on that rationale in Una's trial only highlighted the absurdity -- especially when Admiral April claimed he would exclude Una to prevent genocide.
On the one hand, the writers may be trying to create a straw man out of a weird part of Star Trek lore so they can have a civil rights issue in Starfleet. And that's fine. From an in-universe perspective, though, I think we can discern another reason for the ban on genetic engineering -- the Klingon Augment Virus.
There was a ban on genetic engineering on United Earth, which is understandable given that it was much closer to the time of the Eugenics Wars. Why would that remain unchanged when more time passed, more species joined, and more humans lived in places without living reminders of the war? [NOTE: I have updated the paragraph up to this point to reflect @Value Subtracted's correction in comments.] The answer is presumably that they needed to reassure the Klingons that something like the Augment Virus would never happen again. Hence they instituted a blanket ban around that time -- perhaps in 2155, the year after the Klingon Augment Virus crisis and also, according to Michael Burnham, the year the Geneva Protocols on Biological Weapons were updated.
That bought the Federation over a century of peace, but after war broke out due to a paranoid faction of Klingons who thought humans would dilute Klingon purity and after peace was only secured through the most improbable means, they doubled down on the ban. Una's revelation provided a perfect opportunity to signal to the Klingons that they were serious about the ban -- hence why they would add the charges of sedition, perhaps. Ultimately, an infinitely long speech and the prospect of losing one of their best captains combined to make them find a loophole -- but not to invalidate the ban or call it into question. This Klingon context is why April, who we know is caught up in war planning of various kinds, is so passionate that the ban exists "to prevent genocide" -- he's not thinking of people like Una, he's thinking of the near-genocide they suffered at the hands of the Klingons.
This theory still doesn't paint the Federation in a positive light, since they have effectively invented a false propaganda story to defend a policy that has led to demonstrable harm. But it makes a little more sense, at least to me. What do you think?
It's important to remember that Earth has an outsize influence on the Federation. The capital is, and always has been, there, and will continue to be until such time as it secedes entirely from the Federation after the Burn. The Academy is there. Starfleet is headquartered there, and grew out of United Earth's space service. Most of Starfleet is human, most Federation colonies are human. Azetbur was mistaken to call itself a "Homo sapiens-only club" but the fact is that from the beginning, as the only planet with friendly relations with Vulcan, Andoria, and Tellar Prime, as the very reason the Federation exists... Earth found itself with a power dynamic that highly favored it.
As such, I don't think it's too surprising that a specifically Earthican problem could weigh heavily on the Federation, even as it grew larger and more cosmopolitan.