How far in human biology can I go without high school chemistry?

To the front door maybe, but not actually through the door.

you don’t really need chemistry for the material but it helps quite a bit.

Here in the US you can take an intro Biology class in college without having taken Chemistry in high school. That’s about it.

In many universities, there are core science components which consist of one or two chemistry semesters. So all you can get done is that core biology class (or classes) before being hindered by a pre-requisite.

Not very. There’s an awful lot of chemistry going on in the human body.

You can test into (challenge) any course. You have to be good at calculus though.