Is it bad to use 5w30 synthetic instead of 5w20 synthetic for a 4 cylinder Honda?

No.

Addition..

If you are looking for better engine protection and are not worried about the minuscule loss in fuel efficiency use the 30 weight oil. A lot of manufacturers "RECOMMEND" a 0W20 or 5W20 oil... this is really to get the car to maximum fuel efficiency here in America.

Car companies love to claim they have the most fuel efficient vehicles. One way to meet EPA's MPG requirement is to use a lower viscosity oil such as 5W20.

You go to Europe same cars are running a 40W oil, and they are changing it at 10K