Okay I have rooted cuttings in plastic cups with small roots showing and leaves on top I have moved them outside to start hardening off so I can pot them up.. My question is I am concerned with the delicate white roots and the sunlight will the sunlight kill my roots???? Should I be protecting the roots from sunlight or not worry for the week I am waiting to pot them up???

In my opinion you are taking risk by taking a rooted cutting in a plastic cup (if less than 32 oz) outside exposed to the sun or warm temperatures because of the small soil volume. The soil can heated up and dry up faster and a little lack of attention can cause problem. If there are visible roots on the side of the cup then you can transfer it to a pot (32oz+ to 1 gallon), then keep it is shade and humid environment. If you believe there are not enough root then have patience with it and keep it inside to grow more roots.
May be I am more cautious than necessary but that is the way I do it.

Ditto. Patience is a virtue in rooting figs.  I go from rooting to 1 gallon pots, in shade with just a little filtered sun and good humidity till I am sure they are stable. Some go back to the greenhouse for a few weeks to progress a little further. esp if they are one of a kind cuttings. I have my latest 1G pots under my large tangerine tree (lots of shade, a little filtered light, and sheets around the edge of the canopy to limit early and late sun. I mist  a lot and water as needed, wetting the canopy of the tree and the sheets to add humidity. It is hard for me to get too much humidity. Some places, like the Gulf Coast don't have that issue.