Coming from someone who has injured their Glute medius by having chronically weak muscles and sitting at a desk job----
It's essentially the equivalent of a rotator cuff shoulder muscle. It is a very important muscle that helps externally rotate the hips and stabilize your body during walking or just standing on one leg.
At bare minimum, a lot of people should at least do stretches with bands for rotator cuff and glute medius, such as clamshells, band stretches, piriformis stretches, and maybe some lateral walks. Strengthening this muscle will lead to huge increases in your squat and deadlifting capabilities. From personal experience if you sit down all day, I found it amazing to get up every hour and do a quick set of 20-50 body squats, or at bare minimum walk around for 5 minutes(but the squats are a lot quicker if you're busy).
I've had glute medius injuries before, like Melvio said in his answer, no one hears about it or does anything until they injure themselves. If you have a sedentary job or desk job, I think it's a necessity to also work it out, probably a few times a week. It'll become very weak and eventually you'll get injured doing something incredibly easy that you never thought you would get injured doing. These muscles can take a long time to recover, and it put me out of the gym for my quads for a year, because a few months was just healing, and the rest was stretching and working back to where I was. The muscle prevented me from doing deadlifts or squats but I could do leg extensions, RDL's, and leg curls.
You can target your glute medius specifically while also building the rest of your body by the way. A favorite of mine is bulgarian split-squats, and at the end of each set at 3/4 of the way up I hold the position for 10 seconds. I also make sure my shin is more vertical and my torso is vertical. These two tricks blasted my glute medius. Lunges are also great, any one-legged squat variation. You can also do glute hip thrusts with a band around your knees to force external rotation. Doing these tricks will train your GM without you having to specifically make a GM workout, you can just add a couple hip abduction/adduction exercises and be on your way.