Yes. It is a safety issue. Buy a new battery. Put that one in a plastic garbage bag to contain the powder. You can drop it off at the place where you buy the new one. They will make sure it gets recycled. Lead acid batteries are very recyclable (people will even pay you for old non-functional lead acid batteries). If you just want to get rid of it, you can probably drop it off anywhere that sells lead acid batteries (call first to make sure).
What has happened is that the plastic housing has cracked, electrolyte has leaked out and evaporated, leaving white crystalline solid material behind. That is the crust.
The battery will now not deliver full capacity, and charging and discharging the battery could potentially be dangerous. Discharging could lead to overheating. Charging could lead to overheating, liberation of hydrogen and even in a worst case some type of explosion.
There is also a chemical hazard because the elecrolyte is corrosive and contains lead. You should try to keep that crust off of anything you care about because it may absorb a little moisture from the air and dissolve or damage whatever it comes into contact with.
Lead acid batteries use an acidic electrolyte (sulfuric acid). Alkaline batteries use a basic (as in pH > 7) electrolyte. So they are different even if they look similar when they dry up.