Footwear for June ?

Where are you planning to go in June so we have an idea of the seasonal weather forecast in that area to better advise you.

If you're not going to be trudging through mucky fields then I don't see any need for waterproof footwear.

Depends............weather could be chilly compared to what you are used to for June (depending on where you live). Also, if you would typically wear waterproof shoes if you were walking outside in the rain on a possibly-chilly day, then you might be more comfortable having shoes that keep your feet a little warmer.

If it were me, about a week or two before you leave for your trip, check the weather forecasts for the cities in which your tour will go, and if a lot of rain is predicted (along with cooler temps), then take some shoes that might keep your feet dry.
Otherwise, I would just pack a really comfortable pair of shoes with a back-up pair (to change into if the primary pair gets wet).

Hope that helps.

We visited Ireland at the end of August, and it was chilly with light rain off/on. The wind is what I found more unpleasant than the rain.

Definitely have a light hooded rain jacket (and one with a hood that projects out enough to provide some cover for glasses, fi you wear them).

Whatever you wear at home on a rainy day should suffice.

I'd agree with Robert. You're likely to encounter some rain. Wear something you would wear out on a rainy day at home. Completely waterproof isn't required unless you are tromping around in the mud.

hooded rain jacket (and one with a hood that projects out enough to
provide some cover for glasses

or do as we do: wear a baseball cap under the hood. Protects your glasses and keeps the hood away from your eyes.

I have been to Ireland twice and had wet feet both times - March 2019 and July 2015. Don't underestimate the wet and wind that can occur even in the middle of their so-called Summer. - It doesn't take much to get wet feet in Ireland. you may be hopping on and off a bus - but Irish rain has a sneaky way of making things just plain soggy. I lived in London for 23 years - I can deal with rain - but Irish rain comes in a variety of sorts at any time of year.

Margaret

We spray all of our outdoor shoes with a waterproofing product...works great.

If you spray, make sure you give the shoes plenty of time to air dry. The chemical needs to both soak in and dry completely to work. The stuff I've used to waterproof has a chemical odor for awhile after you spray it (Maybe they have better sprays now?). It's not something you do as you're heading to the airport.