Imagine that I did a small favor for you such as making change for a $20 bill. You say: “Thank you.” I respond with “no problem.”
Would you find my reply to be ungrammatical? Would you consider it rude? According to this list of grammar gripes on the NPR site, some people would.
A couple of things about that item in the list surprised me. First, that NPR would include it as matter of grammar. Second, that people continue to edit casual conversation, including personal email.
To my ear, “no problem” is fine between friends or family members to acknowledge gratitude for a minor task. It doesn’t break a grammar rule to say it or write it.