Figuratively, the law gives people the energy to protest, and thus it is "fuel" for the demonstrations. "The protesters were getting tired and the demonstration was running out of steam. It might have ended peacefully, until the police arrived and added fuel to the fire by using their nightsticks."

It could be replaced with "causes".... it's the sense that the law is creating/enlarging the demonstrations. In the same way that you pour fuel on a fire to make it bigger, you "fuel" something by making it bigger. Here are a few similar examples. The protests were fueled by the governor's decision to pardon the convicted felon. The president decided not to sign the free trade agreement, fueling the anger of conservatives. Fueled by their rage, the university students set fire to the dean's office.

It means that the LGBT law causes/generates/stimulates manifestations for and against.