Using relay to switch power supply
Conservative engineering practices, and my own "school of hard knocks" experience say that you have to size the relay for the inrush current, because even a brief surge can weld the contacts, in which case the relay is stuck on and could lead to a bad safety problem.  But don't decide by looking at the brief ratings in a catalog. Look at the data sheet and see if there is an inrush rating that is higher than the continuous duty rating.  Motor starting contactors are an extreme example of this. They have contact materials that resist welding, and their ratings reflect this.
Another approach that you see in large power supplies is a separate set of contacts, in series with a power resistor, that are closed for a second or so before the main relay closes, to more gradually charge the filter capacitors. Sometimes referred to as a "soft start" circuit.