Melted rubbery/plastic spider in oven

Throw it away.

When synthetic materials like plastics burn, they generate a lot of bad compounds, some of which are odorless, but many are carcinogenic.

While we can't eliminate all sources of carcinogenic substances in our lives, this is one instance where one can clearly avoid ingesting carcinogens because the choice is available.

Clean your oven thoroughly and run it once more after the cleaning with nothing in it (let's say 450 degrees for an hour after the oven has reached that temperature).

As long as you enjoy cake that tastes like burned rubber, it's probably fine. Use a no fume oven cleaner so your self clean cycle won't send the smell through your house.