I absolutely loathe poor customer service and would definitely let the manager know about this member of staff!
I worked with the general public for almost thirty nine years and was never rude, or even short with anyone, no matter how ill, tired or angry I felt!
If people choose to work with Jo/Joe public they have to accept that 'the customer is always right' even when the customer is quite clearly wrong, not in the OP's case of course!
If I get exceptionally good service, I always comment, and if I get poor service, I let them know that too!
I always try to brighten the day of anyone who serves me, no matter the circumstance, the public can be very hard work, so if I can make serving me a pleasant experience, it might improve their day in a tiny way!