How "suspicious" does someone have to be in order for the cops to care?

Mail theft is not a police matter. It’s a federal crime. I’d suggest contacting your local post office to ask how to report incidents like that.

I really can’t imagine a postal empoyee rushing out to your house to tackle an offender caught in the act, so I don’t know how that’s supposed to work.

Well, obviously was not expecting an urgent response. I used that as an example, because to me that is suspicious but I was basically told it was not. So it made me think, if the cops find that normal, what is not?

I’m wondering if the police would think that possibly the person had permission, like if the family were away and asked someone else to go pick up their mail, or maybe the police assumed that the lady was one who lived there? I don’t know if they know who lives in every house. I am guessing they don’t.

Yes it is strange and I might report it to the police not because I expect they will do anything about it but because it may be part of a pattern of strange behaviour involving criminality or perhaps illness.

There is probably the factor of how busy the cops are. Yes, someone rooting through your mailbox is suspicious. But if the cops are already stretched thin, it isn’t high on the danger list. @flutherother has the answer. Go ahead and call the cops anyway to report it. They may not do anything, but at least if it later shows up that this woman is doing more than just looking in mailboxes, there is a report about it.

Depends largely on skin colour. If your skin is dark enough, even normal activities will be seen as “suspicious”.
The director of “Black Panther”, Ryan Coogler, was famously arrested at a bank for trying to withdraw money from his account.

Small crimes don’t attract attention.

These questions are always hilarious. Like you know there’s robbers and home invaders, car thiefs, murders and rape, right?

Do you really think anyone has time to pursue a most likely white person going through mail?

No I had no clue felonies existed. I expect the cops to drop everything and handle my case. I am totally not asking a question about what qualifies suspicious behavior.

I also totally did not just use the mailbox as an example, because I feel that is suspicious but the cops disagreed. I had no other examples to give.

Anything to do with the mail, is also a federal offense...