I see your point, but I strongly desagree with you because several reasons.
Unisex names are becoming more and more popular in the United States and by extension in other English speaking areas, but not in the rest of the languages or places (and that is the case of the Welsh language and Wales).
The use of names from a foreign culture should respect the conventions of that culture, if not this can be seen, and probably will be, as an ignorant or/and disrespectful action and can carry not the sympathy of the native speakers or people from that culture but exactly the contrary. I discussed that several times with Catalan, Basque, Russian, Irish and Welsh people and there was a general assent about that (the transgessed conventions varied from culture to culture).
Obviously, while the person with the wrongly used name doesn't interact with people from the original culture, there is not any problem; it will be simply a strange/inusual/odd name. But when the interaction comes, it is very probable that the reactions will be negative: hardly with words to his/her face, but sure from behind as a joke among the native speakers and reinforcing any cliché about the intelligence/culture/cleverness/education... of the people from the culture to which the wrongly named person belongs. The more strong the stereotypes, the more easily the mistake will be mocked and used as proof of that stereotypes. That is true not only for the names, of course, but for any cultural piece.
And about "(...) while listening is nice and helpful, it is ultimately your choice and that is their problrm if they don't like that name.", that is true, but that is a two ways streets: you (general you) can do publicly whatever you want (always legal) and the rest of the world can thing and comment whatever they want.