Largely a company can choose their customers; they’re not forced to transact with anyone. There are some exceptions of course, largely based on the reasons for not transacting. Being publicly traded doesn’t really matter here directly.

I'm curious, do any kind of discrimination laws apply here?

They do, and that's what I was getting at when I used the qualifier "largely".

Why would being publicly traded keep them from choosing their customers?

I assumed that it's his/their fiduciary duty to maximize profit, and if the current excutive team doesnt do that, they will be replaced with a team that will.

Execs have wide latitude to do their jobs, and considering the current circumstances I could see them deciding that declining to take police as customers would be better for the company long term.

This would be a very defensible decision legally (not a lawyer). You're right that it could plausibly lead to some sort of shareholder rebellion, but I'd be surprised.

Here's Amazon making a similar decision: https://news.ycombinator.com/item?id=23482406