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.

As you may know, Latisse is the first and only FDA-approved prescription treatment for inadequate or not enough eyelashes, growing them longer, fuller and darker.
The recommendation to use Latisse at night has nothing to do with safety but rather with the goal of prolonging the amount of time the Latisse remains on the area where it is applied. Allergan actually recommends using Latisse at night and I think it is a good idea to follow the company's recommendation. But if it is not possible for you to apply it at night, then you can apply it during the day; you may just not get as much benefit out of the treatment.

Latisse is a reformulation of Lumigan an anti glaucoma (high pressure within the eye) medication ALSO produced by Allergan (maker of Botox etc). Lumigan was used as eye drops applied to the eye during the day (during its use the hair growing effect was discovered). The use at night has nothing to do with safety and everything to do of prolonging the contact time between the edge of the eyelid / lashes with Latisse.
WHY wouldn't you want to use Latisse at night as the company recommends?
If you want to get full benefit you SHOULD follow Allergan's recommendations.
Dr. P. Aldea

Allergan, the company that makes Latisse, recommends night time use. Part of the reason for this is that the study performed for approval of this drug, mandated night time use. Generally, drug companies will stick to the same usage as was indicated in the study for which it was granted approval.