Though this is a common terminological distinction (at least in animals—this usage of “intergrade” is rare, in my experience, among botanists), I’m not aware of a reason why the two cases should be treated differently either in terms of the nomenclatural codes or on iNaturalist.
It may be wise for iNaturalist to have consistent formatting rules, though. Omitting the genus and specific eptithet (e.g., Setophaga coronata coronata × auduboni) implies that the genus and specific epithet are identical for both parental taxa. This kind of omission can be ambiguous, though, as in Setophaga coronata auduboni × townsendi. This formatting seems to imply that the parental taxa are both subspecies of Setophaga coronata, but there is no Setophaga coronata townsendi. I assume the second parent is Setophaga townsendi. Formatting the name as “Setophaga coronata auduboni × Setophaga townsendi” would remove the ambiguity.
If one of the parental taxa has no subspecies, just give the binomial: Setophaga coronata auduboni × Setophaga townsendi.