Booking rooms in advance in mid May

You will be able to find a room. It may not be your first choice in terms of location, price, or amenities, but you should be able to find a room.

Agree that you would be able to find a place to stay in all of them, but booking at the last minute you won't get the best options (in any). That said, I would suggest that how far down the list of compromises you will have to settle for (when booking last minute) wont be equal in these places. Each place has a different set of variables: how much tourist interest (number of people competing for available places), and how many places there are to stay that everyone would be competing for.

Of those mentioned, I'd expect Dingle to be the hardest to book last minute (pretty high tourist interest, smaller town with fewer options for sleeping). Galway gets lots of tourists, but it's a much bigger town (it's a city) so you would probably do better there at the last minute. Kinsale and Kenmare would be somewhere in-between on the size/competition scale. The smaller the place, the more willing to compromise you would probably need to be.

We just went in May, it was a fantastic time to go!

You have good advice so far. I think it also depends on which locations you will be in on the weekend, those might be more challenging to get last minute.

My husband is more of a "let's wing it" kind of person, but as we age, he has found it to be less fun. Unless, you have a lot of down time built in, Ireland travel tends to be a very on the go, in the car, stop and start experience.
I wouldn't want to be be weary at the end of the day and start my search for accommodations then. Maybe a combination of set reservations and spontaneous would be wiser. Also, always book places with generous cancellation dates, then you can pivot during the trip.

Whether Ireland or elsewhere, the trouble with "spontaneous" is the time you spend on your trip looking for accommodations instead of sightseeing, transiting, or whatever else you'd rather be doing. It's true that booking ahead can lead to disappointment when the place doesn't live up to its website or advertising (they use those fisheye lenses for a reason). Also true that you needn't spend much time searching if you're really ready to stay anywhere, like the first place you see.

Based on last year's trip, I'd say mid-May would be a time to reserve ahead, especially in Dingle. Maybe not before you leave home, but at least a few days before getting there (taking time away from whatever else you'd be doing on your trip).

I think the Covid travel rebound has made 2022 tougher for "spontaneous" than ever. I make my airline reservations on the day the airline opens bookings (usually 11 months in advance), then immediately book a car, and I book lodging as soon as possible, which is often about six months. I'll drag my feet on ferries till maybe 60 days. I often re-look at lodging choices, and I never find the price has gone down, and rarely find places I consider "better" becoming available. I always use "free cancellation' that allows me to make itinerary changes over the six months that the plan gets to 'bake". I'll admit I'm on one end of the spectrum.

We did our first Ireland trip with no reservations except airfare, and we found ourselves in hostels (nothing wrong with them unless you're a light sleeper or need to pee a lot) or scouring the countryside at dusk. That was pre-internet so it may be a useless data point. I think the internet has made it worse for spontaneous travel.