This question doesn't have a simple yes or no answer. Guitars with thick, durable finishes generally won't have any issues, but it's important to be careful with guitars that have a delicate finish, such as a thin nitrocellulose finish on many Gibson or Fender guitars.
There are many situations where a finish can get damaged. To be safe, it's always best to store your guitar in its hard case. We can also make your guitar strap with plastic parts instead of metal parts. If you're concerned, you can also ask us to create a custom, non-adjustable strap without metal parts. This will ensure nothing on the strap can compromise your guitar's finish.
A standard strap with metal parts always poses a risk to a guitar's finish. If you have a "relic" guitar, you might not be concerned, but it's something to keep in mind.