Safe to Wear Latisse During the Daytime?

It may be but the manufacturer of the product, Allergan, advises application at night, after you've cleansed your face and before you go to bed. All clinical trials is based on this application routine.

There is no real reason (other than there not being other eye products like mascara on) that you couldn't apply Latisse during the day...your eyelashes can't tell the difference in time of day.

I think it is absolutely safe to apply Latisse in the morning and use during the day. Yes, it is off label, and in some patients, the risk of red irritated eyes will be higher. You have to try it to see which time of the day works best for you.
All the other potential problems (rubbing the eyes, tearing, etc.) may very well happen at night as well, except you don't know that it happens. It is very easy to apply it in the morning, let it dry, and then apply your make-up. This is what I do personally, since I am too tired at night to remember to apply it.

Night application more logical, at night there is no mascara ,no make up nad no possibility of sweating that can diffuse the latise on the skin which you do not want to have

Latisse is meant to be used on clean skin. Since most women use eye makeup of some type, that means you may not get the best application if you have eye cream liner or mascara on. Plus, blinking, rubbing, etc during the day could potentially transfer more of the product into the eye.
You'll likely get the most benefits by applying at night and avoid increasing any of the small possible side effects as well.