You mean the solider who saw what happens when a list of everyone who is considered "other" is ordered and maintained by a government? All because, Tony "I am a gift to God" Stark and Bruce "Couldn't Say No" Banner created a nigh unstoppable police force with no oversight?
IMO, you're not wrong, but Magneto is the better portrayal.
Magneto was right all along about the persecution of mutants. Tony Stark and Captain America disagreed on a "who watches the Watchmen" level in the movies.
Stark thought that heroes had too much power to act without the approval of some higher authority, and the Captain believed that they should be able to act when and where they could without needing permission in order to do the most good. Magneto looked at the number he had tattooed on his wrist as a child in the camps and said, "Never again."
Tony also had the issue that he felt guilty over his failed plan to protect the world that was pretty authoritarian.
I don't think cap would have been against all oversight, but the one presented was very narrow minded and slow to act until more drastic decisions had to be made, like nuking New York.
It's far from my only understanding of it, it's just the first thing that comes to mind for what might make him averse to a list of "others" being created
He probably would have also seen what happened with the US's registry of Japanese people, which didn't go great for them either