I agree that Breeders are an odd choice for a representative - as representatives they're meant to represent interests in an alien environment, to be a go-between for their potentially less diplomatic faction members - not as an exaggerated display of their "alieness". Personally I like the fact they look horrific - but not that this is something worn openly. If the argument is that Ta are needed as they're the most diplomatic then they would try to counter any issues faced with this.
I think a good solution would be to provide Ta with an "encounter suit" to hide their appearance from everyday crew. If you've ever seen Babylon 5, there are a species called the Vorlon who have a similar issue with sending representatives - so their ambassador wears an "encounter suit" to mask their appearance. This keeps an air of mystery about what they look like under the outfit (retcon that they're rarely seen outside the suits when in alien space) and keeps them looking horrific if the suits are ever removed.