Should I apply a screen protector to my MacBook Pro 13

Adhesive damage is permanent and can only be dealt with by:

• paying US$500-700 for a new display assembly, or
• living with an ugly splotchy display.

Even the ones that adhere by surface tension or static have damaged displays. See:

Using a camera cover, palm rest, or keyboard cover on a Mac notebook - Apple Support

Since no MBP is touch screen, I can't imagine what value a screen protector could possibly offer? I'm a big fan of screen protectors on devices which you touch. But do not and have no plans at all to put one on my MBP.

There is one situation in which a screen protector could provide a benefit. And that would be needing a privacy protector on a device which is often used in public spaces, where you would not want someone to be able to see anything on your screen from an angle.

You're welcome.

Watch for any protector that has adhesives. The screen coating is sensitive/reactive to certain chemicals. But a privacy screen that slips-over should be safe as long as it is removed before closing.