Question Are Waterproof Shoes a Must for Ireland in Late May?

We're gearing up for a 'Week in Ireland' tour in late May and have already packed raincoats. Now, we're wondering if waterproof shoes are also essential. Given Ireland's reputation for rain, does anyone have experience traveling there during this time? Did you find waterproof shoes to be a game-changer, or were regular shoes with good socks sufficient? Any specific brand or type recommendations would be super helpful!