For the soap scum, I have tried Thieves Oil, which is my absolute favorite product for cleaning the tile floors, but it is pretty much useless against soap scum, even at 100% concentration.
Iit was time to find a middle of the road between the old faithful non-green products and the green ones that aren't too effective. After a lot of label reading at various stores, I settled on Clorox's GreenWorks Natural Bathroom Cleaner.So far, it works well. It just took a few squirts onto the soap scum and it went away. However, when it comes to the bathtub, it still needs scrubbing help from scouring powder. It's fine on tile and shower doors, though.
It's important to note that while it is "natural" and biodegradable, it's still not as natural as it could be - it does contain some chemicals. However, the other high-powered soap scum removal product I was looking at in the store that claimed to be green also had a warning "use only in a well ventilated area and do not inhale". WHAT?? How can that be healthy??