What are the skater's reasons for wanting the item? What are the coach's reasons for disallowing it? If you can't discuss it and come to a solution that works for both parties, I'd consider a coaching change.
That said, as a coach, I would argue against a traditional bike helmet (but would allow a multi-sport or hockey helmet - safety issue, the bike helmet isn't designed for skating falls), and I wouldn't allow anything that restricted the skater's natural movement without a good (medical) reason. I have no problems with non-restrictive padding, appropriate helmets, or an ice halo-style headband. Although above a certain level, I'd probably not want them worn for test or competition unless medically necessary, but I haven't really thought about it enough to know what level that would be...