Vaccinated students will not be continually harboring spike proteins after vaccination – the vaccine induces spike proteins, which are then recognized, neutralized, and destroyed by the immune response. Your students will likely encounter far more spike proteins (attached to replicating viruses that can make them sick) at colleges where the students and the rest of the college and surrounding community have a low vaccination rate.
Of course, if they want to play COVID-19 lottery, they can go to college in states like Alabama or Florida, where the state governments disallow colleges from requiring COVID-19 vaccines.