How is this different than trigger locks mandated by the federal government? How is this different than federally mandated background checks?
Now, you come back with "they're also unconstitutional", we're done on this thread.
Background checks at least are a "regulation of commerce" (so what if it's not interstate; that part seems to have been forgotten about long ago). Even trigger locks can vaguely be thought of as a commerce regulation, on the grounds that someone might hypothetically sell the thing without a trigger lock (specious reasoning, I know, but that's what we've come to expect from the court's "interpretation" of the commerce clause).
But rules mandating how you store your weapons have nothing to do with commerce. They fall in the same category as the "law" that was struck down in Lopez.