Yes, of course you can. It has been proved safe by many pioneers like Galileo. If it had been bad for eyes, Galileo would have been blind or developed eye problems. As a matter of fact, he became the first human to look at the moon through telescope and watched the universe.
If you want to watch the moon clearly enough, you may need 20 times of Magnification telescope. You can see the details of crater on the moon slightly.The best magnification will be 40 times, as details are clearly showed and it won't be affected by the air.
Yes, you can use telescope to see moon because of the protection from the lenses at the telescope. It is safe for your eyes. The mirror set in the telescope will be with the anti-radiation from the moon light. Your eyes will not get hurt when you look at the moon. During the daytime, you should wear the sunglasses to protect your eyes from the uv rays if the sunshine is strong.
It is no problem to see moon by using a telescope as we all know that the light from moon comes from the reflection of sun not itself, which means the moon can not produce light like sun. The light from moon is mild for eyes to accept. However, you can not see it for a long time in the all dark around or it may hurt you eye sight.
So just enjoy the moonlight!