I'm a nomad and I converted a lot of my wardrobe to wool with brands like Wool and Prince and Unbound. I can wear a shirt for a long time before it needs dry cleaning.
I find dry cleaning to be cheap compared to the time I would spend doing laundry activities.
Ironing an expensive dress shirt with a rusty iron at an Airbnb is not something I want to entertain.
I haven't found a good solution for workout clothes though so I usually stay in an Airbnb with at least a washer.
Not sure if there are analogous workout shirts and shorts but the ExOfficio Give-N-Go boxer briefs are the most travel friendly item I own. They're sorta like Under Armour material but even thinner and lighter so they can be hand washed or air dryed insanely fast. Definitely looking to get more clothing that fits in that category.
More info / Wirecutter review: https://thewirecutter.com/reviews/best-mens-and-womens-under...
The other big annoyance about living as a full-time nomad is laundry. So far I've managed with a mix of laundromats, laundry shops, and the occasional hotel laundry when it's reasonably priced (rarely).