Why is rhesus incompatibility an issue, while there's no blood group incompatibility?

Factual Questions
1

I’m refering to parents having different rhesus factors. If I’m not mistaken, it’s only an issue if the mother is Rh- and the father Rh+ and normally only for the second and later pregnancies. Correct me if I’m wrong.

I believe I get how it works, but what I don’t get is why, say, an O+ mother having a B+ baby isn’t an issue at all.

2

The short answer is that it can be an issue. ABO-HDN wiki article should answer most of your questions.

The gist of it is that anti-A and anti-B are usually IgM antibodies, which do not cross the placenta, while anti-D (I guess you could call this anti-Rh factor) is IgG and crosses easily.