Rather presumptuous on this point. Shras describes his people as a "violent race" in TOS, indicating that they had not been forced to renounce their more violent ways to participate in the Federation.
Humans, Vulcans and probably lots of other Fed species can be described as violent races as well.
Why? The whole point of the UFP is that disparate groups and members can come together and work together for the common good and use mutual cooperation in spite of differences. Even in TNG abandoning trials by combat or death penalties are not exclusionary factors for interaction with the Federation and the Enterprise crew work within the cultural norms not excluding them from participation.
And thank you all for correcting me regarding Ligonians from Code of Honor. Yes, that was the race I was thinking of.
Regardless, I disagree with the categorical dismissal of "it wouldn't be tolerated" which seems rather against the principles of the Federation.
Some of the most important principles are shared values, laws, civil rights, which doesn't mean every member has to give up its cultural distinctiveness. The Federation doesn't tolerate the death penalty; They refuse the membership application of the Angosians because their veterans are mistreated; Bajor would be refused if they kept their caste system; During the Data vs. Maddox trial, the judge points out, "We have rule of law in this Federation. You cannot simply seize people and experiment with them to prove your [Maddox's] pet theories." This is applicable to the Andorian practice too, you cannot force people to participate in a life and death fight for personal vengenace.
The only way I see this tradition may be maintained is if the (mentally healthy) accused can refuse to fight without any repercussions. And of course it should not replace a proper trial, e.g. even if a suspected murderer wins the duel, they must still be taken to court.
The Andorians we see last week in Envoys still carried around with the the ceremonial bladed weapons, and wielded them in the bar fight. So if 24th century Andorians still carry bladed weapons around with them for personal defense, I doubt they've abandoned their ceremonial combat rituals either.
"It's an ice-miner's tool. Andorians play with them as children." (ENT "United")