What's worse is the opposite: when a system tells you that your password can't have a certain character in it.
I don't mean like ♥ or anything. I mean like a period, semicolon, or space.
Which indicates to you that: No, the system is not merely hashing your input and storing it in a database somewhere to be compared to at a later time, or at least protecting it with reversable encryption.
No, the designers of the system are passing your bare password into an API that is going to potentially parse the password as part of a larger construct, in which certain characters could trip up the parsing of that argument string. Why else would they feel the need to input validate the password? Clearly a bug showed up in testing where passwords with certain characters caused issues in some subsystem... :-(
Your password is passed on the command line to some program. Or it's being interpolated into a non-parameterized SQL query. Or worse.
It makes you wish you didn't use the same password for your bank website or email.