Isn’t voting supposed to be private?

I can’t remember if they’ve done this in the past–but–today when I voted, they gave me a card that said my party on it. The cards were color coded. I understand that I can only vote my party, but I really don’t want all the other voters to know which party I belong to. Isn’t that kind of the idea of being able to vote the way you want with privacy? I switched my party in the last presidential primary and haven’t switched back yet. I don’t really want the Democrats OR the Republicans to know which party I am right now.
What do you think?