Not sure why anyone should let "cultural stigma" have any influence on what they do. Who cares?
As for sidewalks being safer than streets, that is a myth. The reality is streets are much safer for bicycles. This is a well covered subject, Googling "safer bicycle street sidewalk" brings up a lot of info. The main reason is drivers are not expecting anything on a sidewalk to be moving at bicycle speeds, so cars turn in front of bikers much more often.