Hair is biodegradable, like food and human wastes, so is basically no problem. The only difficulty is that hair tends to gum up with soaps and form sticky clots - think of hair in the shower drain at home. Long hairs are the worst, while short bristles from shaving are probably of little or no concern. Your shower is far more likely to produce clogs than razor trimmings in the sink.
When you have the opportunity, i.e. a sewer connection and plenty of city water available, use plenty of water in the sinks and commode to flush all your drains well. Your RV waste water system uses the same size pipes as a home, but low water volumes and possible lengthy times between uses can let crud accumulate in an RV system that would not happen in a house.