So why can't he register himself as a Democrat?
Vermont doesn't have party registration, so if that is your standard then there are no Democrats in Vermont.
The entire Vermont Democratic party will have to be purged and disbanded, and the state given over to Republicans, since there are no Democrats.
Also there are no Democrats in any other states such as Texas and Ohio. And over in Virginia, the Democratic VP nominee of 2016, Tim Kaine, is not a Democrat.
Barack Obama was also not a Democrat at the time he ran for the Presidency, though now I suppose he is a DC resident, so he has probably now joined the Democratic party now that his Presidency is over.