A HOME banwave has been reported, and as of time of writing, it apparently is still ongoing. It restricts access to HOME accounts that may have, and not limited to: god egg, bad eggs, shiny variants of shiny locked mons, impossible Gmax mons, impossible moves (not Hydro Pump Drillbur nor the GO Alolan transfer mishap).
Furthermore, there are reports indicating certain URL nicknamed mons are restricting from trading.
Anyhow, do release all illegal and impossible mons, as well as any Nickname/OT that has a URL, before you get caught up in it. Reports indicate that while your console isn't banned from online usage, it cannot make HOME accounts ever again (even in other profiles). This could be a console restriction or IP restriction, details are not clear at this point.
Given HOME's ability to fix Pokémon in saves, it is presently not known if this capability will be used to restrict the online connectivity of players based on the Pokémon they have in their saves.
With that being said, don't break HOME's TOS ever again.
Edit: Based on preliminary reporting, it appears that the HOME bans are given out to user accounts that interacted with any other HOME account that has high varying IP traffic, and has illegal mons. (Basically, HOME accounts might be shared across several people or interaction with such accounts).
Also, do not confused HOME bans with URL trade restrictions. Not the same thing.