Is there such a thing as a rain jacket that's breathable enough for summer? I'd be inclined to just wear the lightest, quickest drying shorts and jersey I could find, pack some good clothes in a waterproof bag and skip the rain wear.
The last place I commuted that had fairly frequent summer rain was the Bethesda/Wash DC area. I tried an ultra-lightweight poncho, small enough to pack into a jersey pocket, and while it was comfortable enough in the chilly springtime, it was miserable in summer heat and humidity. I just got wet in summer, hung my shorts and jersey to dry near an A/C vent or fan, showered and changed for work -- but I was lucky enough to work at the NNMC in Bethesda where we had showers and I could either change to scrubs or the uniform I kept in a locker.
It rarely rained in warm weather in SoCal when I was stationed there so it wasn't an issue. I may have worn that poncho twice in five years in winter or springtime.
I've worn a Shimano Storm Jacket several times this winter and spring and it was comfortable enough in chilly weather. Felt more comfortable than wind chill riding in the 60s. And it's tolerable in the 70s if I bike with very low effort, or for walking. But for most of the year in Texas I'll probably just wear lightweight, fast drying poly baggy shorts and jersey and pack some casual clothes in a waterproof trunk bag if I need to be presentable where I'm going.