science

Will their bodies accept a transplant from another situs inversus patient?

I believe so.

How does the body know which way an organ is oriented?

My understanding is that it has more to do with just getting the pieces to fit together properly. I imagine that some organs are more compatible than others based on their shape. But making sure that there's no "kinks in the hose", so to say, is the important part, as it'd be necessary to ensure that the connecting parts aren't having to be wrapped around in an unnatural way in order for things to fit and stay connected without injury.

However I'll admit that I'm not super well-versed in this. I only know a few bits about the condition after some curious Googling when I played a Hitman mission where one of your targets is a situs inversus patient (and you can optionally "kill" him by destroying a particularly rare right-sided donor heart while he's being prepped for transplant surgery). I thought it was a made-up medical condition for the sake of the game's plot, but was surprised to find out that it's an actual thing in real life.