Don’t gyms usually have dispensers of disinfecting wipes around anyway for before/after contacting the equipment? My physical therapy place is like that.
Eh, commercial gyms aren't as picky about hygiene as physical therapy facilities. The big commercial gyms that I use just have a couple central spots on the workout floor where you can pick up a paper towel and a spray bottle with disinfectant. But utilization of those items by most gym patrons is kind of hit-and-miss.
On cardio days (treadmill, elliptical, and stairmaster), I just use one or two cardio machines. I can give them a swipe on the handlebars before and after. But if it's a weight day, then I'm using lots of different weight machines in succession. That's more problematic. Unless you leave a pool of sweat on the benches or seats, most people (including me) don't give the weight machines more than just a cursory swipe with a paper towel or a sweat towel after using them. If that much. It would take too long to give each machine a top-to-bottom cleaning.
I view the weight machines as similar to being on public transportation: You're going to be sitting on seats and touching surfaces that the general public has been using, and there's just not much to be done about it short of wearing a hazmat suit. But I'm healthy overall (as are most other folks at a gym), and in a way it's good to expose myself in small doses to whatever the public is passing around. It keeps up my natural immunities over the long-term. So I just go with the flow, and the hell with the consequences.
In general I wash my hands first thing whenever I come in the door at home after any errand or outing, get my flu shots, and all that. I haven't had a flu or cold in a decade, so I figure my immune system and hygiene must be pretty good.
If I feel excessivly worn-out or like I might be catching something, I just stay home for a day or two to give myself a break from the gym and maybe tank up on some extra protein and carbs. The break from working out and the food give my body extra reserves to fight off whatever I'm getting, and by the next day I'm feeling whole again and ready to hit the gym for a big workout.
As for older, sicker people, medical authorities are recommending that they may want to self-isolate somewhat during flu season (something you referenced in your spoiler). So if I were older and sicker, I might set up a workout room at home for use during the flu season with a rowing machine or stationary bike and some weights. I've had that kind of "home gym" arrangement in the past, and it's workable. Just turn on the TV or blast the stereo, and crank out lots of reps. But as long as I'm generally healthy, I definitely prefer the size and variety and sociability of large commercial gyms for workouts.
