First off, listen to Andy. I do this for a living (both the design side and the review side), and the question of how to handle review feedback is real and serious. If it's two coworkers who you've worked with for years and know well (maybe Alice is super conservative about everything and Bob is generally carefree, except gets really bothered about regulator feedback nodes for whatever reason), then it's not too hard to handle. If it's a hired gun versus the new guy... who knows, right? And if it's hired gun versus hired gun, well, good luck deciding who's right, who's wrong, who's panicking about a waste of time, and who's panicking about saving $1M.
Your designer's schematic is, frankly, terrible (even in such a small snippet), and that combined with your description of his behavior gives me low confidence. It is not easy to read, mixes American and European symbols, and leaves off important part numbers and component descriptions. Correctness comes first on a schematic, clarity comes second, and everything else comes later. But correctness and clarity go together, because if you can't understand it, you can't check it (or repair it). Forcing designers to match personal preferences after the fact is a waste of time, yes... but sloppy schematic capture is usually sloppy circuit design is usually sloppy final product. So pay attention!
The relay datasheet (and the one for Panasonic TX relays, a drop-in replacement for these TE Axicom guys) suggests you shouldn't drive the coil this way. I've tested the smaller versions of these relays on the bench and found that they don't appear to care too much, so this will probably work. But it's not what the datasheet says to do, it's drawn really badly, and it's not something I would do in production (though I also wouldn't stop the presses for this). So... your designer is sloppy.