What do people use cookie pans for if it’s not oven safe?

In that picture the pan almost looks like it is made out of plastic, like a plastic tray. What is the material?

These pans are MEANT for oven use, and that's understood, so not on label.
Other things (like washing or other use ) are variable, so have to be noted.
Aside from baking cookies, they are often used for holding cakes or quiches while they bake (to catch possible overflows) or roasting various foods.
Hope this restores your confidence in using this pan safely.

Is it a specific pan that you have? Cookie sheet pans are meant for baking cookies. Do you have a photo you could share?

Unsafe how?
Please tell us more.