I saw a number of people with gray robes and shaved heads while I was in Seoul recently that looked like this:
Is this a religious thing? They had Republic of Korea passports, for what that's worth.
They are almost certainly Buddhist monks - the shaved head and gray clothes (apparently called "gasa") are a mark of their ascetic style of living.
The gray robes worn by a monastic declare that one is a practitioner, and represent the spirit of no belongings, letting go of all worldly desires.