I suppose a lot comes down to how much one believes the book defines their world or they define their world.That is a pretty lame "reskin". Just get the damn owl if u want to have flyby cheese.
I would allow the owl to be reskinned if there was some sort of creativity involved. For example, a red parrot for a pirate wizard or even a toucan or something.
Imagine a player wanted the 10 foot reach of a bug bear but wanted to play a pretty elf anime girl. Or someone wanting to get the free Variant Human feat but wanted to play a Drizzt clone.
Would a GM allow a "race" to be more fluid?
Can I be a "stone elf" who is a member of elves who have the stats of dwarves, total swap, but more the appearance of elves. Not drow. Or maybe an off-shoot of drow with all the specs of dwarves.
Honestly, off the cuff, I would be fine with that.
But, unlike what seems to be a source of contention, it would be a part of the world. Folks would not be assuming "only dwarves have" trait ABC.
Just like, if I allow reskinning familiars, folks dont assume "only owls have flyby."
Imo, if a gm has an issue with flyby attack, they should fix it, up front, before they let a player choose it... not allow it but then stick it to them by disallowing reskin for funsies.