They are still okay to ride until they finish determining whether they want to wear out or just let a road hazard take them out.

The fraying on there might also be from the tire not being sufficiently inflated and the rim is rolling on it. Other members have shown new tires that exhibit the same thing. Never has any said they had a bad experience with them. I'd ride them till they .... after I checked the tire pressure.

It's a local non-profit. You don't really want to beat them up on a set of tires on a used bike that they may have said were new, when possibly they just meant that they looked new to them.

The tires may not last as long as they should, but they'll have a good chance of lasting till you get tired of riding the bike. Unless unlike many people that get a bike, ride it a few times never to get on it again, you truly do get hooked on riding multiple times per week.