No, there are no adverse effects at all to your eyes (or any other part of your body) from using a screen protector. In fact, instead of causing harm to your eyes, screen protectors actually help them.

For instance, blue light from your screen can be quite harmful. UV glare from the sun and other external lights reflecting off your screen can also cause long-term damages to sight. Using a screen protector helps to strongly reduce the intensity of all of these light sources.

By doing so, it relieves pressure on your eyes and helps you see clearly without having to squint. This effect is present for all kinds of devices. It doesn't matter whether you're using a screen protector on your phone, on a Mac, or even a HP screen protector, your eyes will thank you for it.

https://viascreens.com/screen-protectors/hp/, This page has more information on the subject.