What is the best way for one character to check multiple other characters loyalty cards, without knowing who each card belongs to?
Some variations on the Resistance mechanism, that may be more efficient depending on your design:


Let each player being investigated take a "good" and "bad" token from a common stock, then put one of those tokens in a bag and the other back in the stock (in a way that you can't see what they put back.
Use a pair of hand-held clicker counters with the displays covered up. When you get them, you click the one that matches your alignment, then the person doing the investigation gets to see the final counts.
Do it like old-school Werewolf/Mafia, and just have a moderator handle all the secret information.