Depends on how you define safe. If you are going slow enough that a sudden loss of that tire won't cause a wreck, then it's safe to that extent. If you define safe as being very dependable to get you out of the middle of nowhere, because of non cell service and/or extreme environmental hazards such as temperature or blinding rain or fog (and your being stuck on the side of the road) then it's not safe.
Yours in particular, is not safe for the latter since as you noted it has been exposed to UV all this time, or at least however long it's been on the roof.
I would either remove it and do without a spare or get a new one.
You won't necessarily see the damage done by time to an old tire. There can be ply separation and cracking you'd only notice once bearing weight and especially if low on air.
Then again safety is shades of gray. It's safer not to drive at night, when raining, on icy/snowy roads, or in a 20 year old SUV, and to wear a helmet. It's also safer not to buy a new car with un-ergonomic touch screen et al controls, not to conduct phone calls even if hands free, not to have kids or (other) insane passengers, and not to turn the radio up high, not drive when tired, not drive a small car or especially motorcycle, and so on.
If you're against buying a new tire then that old one could still save you a tow bill.