For those protestors that are arrested, most would likely be able to clear their record. Typical arrests for protestors are for misdemeanor level charges like criminal trespass, disorderly conduct, resisting a peace officer, etc. Often times these charges are dropped fairly quickly, as the main purpose of the arrest is usually to establish order in the given situation. If the charges are dropped, then the defendant can expunge the arrest from their record so long as they have no prior convictions. If the defendant receives court supervision, then she will be able to expunge the case as well, but will have to wait a couple years. If the defendant has a prior conviction, or is convicted of this charge, then they will be able to seal the charge rather than expunge.
The concern for an arrested protester is to avoid convictions for violent crimes, such as assault or battery. Convictions for violent crimes are not eligible to expunge or seal. The only way to clear these from your criminal record is through executive clemency (Governor’s pardon).