Disclaimer: I'm in no way an expert on this.
There is some evidence that the shape of the head can be influenced by sleeping positions (see, for example, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3116745/ and http://www.uchicagokidshospital.org/specialties/neurosurgery/patient-guides/head-shape/). The back of the head seems to be especially soft, so if baby sleeps on the back and the same spot on the back of the head keeps touching the bed, that spot might flatten a bit because the skull is still fairly soft in the first months of life. In order to counter that, you're supposed to make sure that the head isn't always in the same position when the baby sleeps, and not keep them in car seats etc for longer than necessary.
However, I very much doubt that this usually leads to serious asymmetries that might lead to problems later. First, it's mostly an aesthetic thing. Second, if serious asymmetries were likely, wouldn't the world be full of people having such problems? Wouldn't we all walk through the streets thinking to ourselves "jeez, what an ugly asymmetric head that guy over there has" all the time?
You can't watch your baby sleep the whole night. When it prefers one side and turns back an hour after you go to bed, how do you fix that? What happens to all the babies of people who have never heard about the shape of the skull being influenced by the sleep position of the baby? Why aren't these babies all growing up with horribly deformed heads?
Personal obervation does suggest that slight deformations at the back of the skull are a possibility. With my oldest child, we took the advice to keep turning his head very seriously, because we were first-time parents and very concerned about basically everything. He happens to have a very nicely shaped head. With the following babies, we didn't have the time to do that. They do have skulls that are somewhat flatter at the back.
That might just be coincidence, or a result of our "negligence". Whatever the cause, it's never been a problem.
could potentially cause the development of an asymmetric posture / skeleton / muscles
I think that everything besides the shape of the head is myth.
As Anthony comments, there can be serious consequences of positional skull deformation (although, as I've said, that's rare - usually it's harmless). This also includes skull asymmetries when a baby keeps putting the head on one side (which I wasn't originally aware of). See my first link or his answer for further details. So keeping an eye on your baby's head shape is certainly a good idea, so you can involve a doctor as early as possible if you notice developing asymmetries or notable flattening of the back of the skull.