It is called “fraflytteraktieavanceskat”. It is a capital gains tax for equities that can be paid at once as if you had sold the shares, or you can delay it by filling out a form every year to the Danish tax authorities after moving abroad.
As for exit tax in the U.S., i really wonder how one could enforce it. So if you left the country and have another passport (otherwise you couldn't drop U.S. citizenship), what can they possibly do to you? I don't think this absurd leftist idea even deserves much attention or comments, someone just said bs without thinking of it much.
You are required to enter the US on your US passport if you have one.
If you wanted to go back (say to the funeral of a friend, or something equally important) then they could detain you until you paid what they thought was due.