Short answer, yes those supportive communities do exist. You need to decide what kind of exercise you want to do or try out.
Most places have running groups that meet pretty regularly and have a wide range of ability. There are also walking, hiking, biking, paddling groups too. I've found a few using Meetup before. Also, you can check out a local running or biking store to see if they know of any workout groups. Sometimes the shops host their own workout groups for free.
Many gyms or pools offer exercise classes and usually have staggered levels (beginner, intermediate, advanced). I've attended a few CrossFit classes at a local gym and every time everyone has been super supportive and encouraging. Plus, some gyms have sports leagues or pickup games that meet regularly.
There are also organized teams that you can join too. I'm personally apart of a US masters swim team and everyone there is just happy that other people show up, regardless of ability or goals. We've had the full spectrum of ability, from just learning to swim to age-group world champions. You can checkout whatever the governing body's website and see if they have a team locator for the sport you're interested in.
Some of the fitness trackers have an ability to share your workouts with your friends. You could possibly use one of those and form your own 'virtual workout group.' If you don't want or have a fitness tracker, there are some free apps out there that allow you to share your workouts with friends (Strava comes to mind). I've used this method before to get myself to complete some workouts on my own.
Side note: I have no affiliation with Meetup or Strava other than that I've used them before. I'm sure there are plenty of alternatives out there.