Diaper bags do not count as carry on luggage so they won't affect your other carry on luggage.
So you can bring your normal amount of carry on luggage and still bring a diaper bag through airport security and onto the plane to use.
You will need a diaper bag if you're flying with a baby or toddler so that you can change diapers on the airplane and feed them.
So the airport doesn't count the diaper bags as carry on luggage for the limit.
That goes for breast pumps as well so at the airport the diaper bags and breast pumps are exempt from the carry on luggage allowance rules.