Here are a few of the more plausible answers thanks to lenpezo.com:
They’re old test coins. In the past, repairmen used them to check out the coin-operated pay phones, vending machines, and laundromat washers they were fixing in order to avoid being accused of stealing. That sounds plausible to me.
They were “house” money. Red quarters are sometimes used by business owners as perks; they give them to their preferred customers for free plays on the coin-operated pool tables, pinball machines and video games. Red quarters were also used by waitresses to “prime” otherwise quiet jukeboxes in order to encourage other patrons to add their own quarters and keep the music coming.
Somebody painted it as a sign of defiance. According to Answers.com, the red coins were part of a campaign in the 1970s to protest New Jersey officials’ decision to increase the toll on the Garden State Parkway from 15 cents to a quarter.
They were once used for free laundry. For some apartment managers, free laundry is apparently a fringe benefit. Landlords will often give their building supervisors red quarters for use in the apartment laundromats. The managers would get their quarters back when the owner or laundromat vendor removed the cash from the machines.