The internet is full of worry when it comes to tire condition. Everyone assumes that the simplest and smallest defect on the outside of a tire is going to cause it to horrifically explode while riding, sending you to an early death.

But nobody seems to remember that tires are not made of 100% rubber. Even on the thinnest front MC tire, there are one or more plies that essentially "frame" the body of the tire so that it retains its shape. The inside of the tire is butyl rubber which helps it hold air.

Sidewall cracks are generally superficial and an indication of less-than-ideal storage or exposure, but not concrete proof that the tire is dangerous to use. The sidewall is there not to hold air, but to protect the inner plies from environmental damage (the plies themselves also are made of rubber for flexibility).

If anything, sidewall cracks are an indication that the bike got infrequent use as the physical distortion of the rubber is what helps it to stay looking new. In other words, bikes that are regularly ridden are unlikely to have superficial cracks as the natural movement of the tire cycles the anti-ozonants that protect it from cracking in the first place.

OP - You have to make the call yourself, but as long as the air pressure in the tire is kept at the BIKE'S recommended PSI then it's unlikely to catastrophically explode one day. Rather, if it fails, it'll be through a slow leak that surprises you one morning.

(I bring up the point about pressure because too many riders ignore the wisdom of engineers and instead run tires at the sidewall listed max PSI.)

Check the date code on the side wall for when it was manufactured (4 numbers where the first 2 represent the week number and the last 2 are the year -- 0415 would be the 4th week of 2015). If the tire is less than 5 years old, I'd ride it for at least once season which will give you time to save up for a new set for the next season.

Hope this helps.