So I noticed this fuzzy fungus on a couple cuttings I have in water. Are they still ok to hold on to? Should I wash them off? Suggestions please... Thanks...

Why do you have them in water? Once they start to rot it's not a good sign. I would hold onto them as long as possible in a moist not wet environment,  but never in water.
If it's warm out there, just stick them into moist soil to allow them to root.

Was trying different methods of rooting and in water was the only I was able to get them to show signs of rooting. I think I know my mistakes with trying to root them in baggies or in moss and will try those methods again next spring. One thing that did surprise me was how quick they would rot in  moss (too wet) but they looked great in water, go figure... These cuttings are from a neighbor and decided to give the water method another try but this time they grew fungus. They were the last couple cutting I was gonna try to root, wanted to try air layering next and started one last week. I wanted to get some practice in just incase I ever find some nice fig cuttings.

 
Had these in water for about 3 weeks and showed signs of rooting, as soon as I put them in soil they busted out with green. I might have just had beginners luck with these.

I Currently use the following method:

Put some moisture control potting mix in a black garbage bag, throw the cuttings in there, and close it.
Make sure that the cuttings are covered with the potting mix inside the bag.
Leave it on the porch in the shade for about three weeks, then check for roots.
Once you see roots,  plant the cuttings carefully in containers.(Twice as deep as the ones you have in your picture).

This method has worked for me with minimum loss of cuttings. Just make sure that the soil is not too wet when it goes in the bag.

Haha, that's too easy. I'm in though, trying it today...

This is easier. Skip those steps and put directly into most HP soil in a one gallon cover with plastic bag. 100% humidity for a 2-3 week's then slowly acclimate to air.

Hi Elfarach, my first year was a total disaster and finally I have about an 85+% success rate. So don't get discouraged, keep on trying.  You will be successful.

Some have had success rooting in water.  I think you need to change the water frequently.  I've had success with the baggie method (damp, not wet paper towel) airing out daily, and also just putting the cutting into damp potting mix and closing in a humidity chamber (plastic bag would work just as well, as brianm stated), but I also air out daily and water only when nearly dry, and very little at time.

Thanks for all the advice everyone, I really appreciate it. Learning tons of new things on here real quick.