I bind at all times except for at home, including exercise (martial arts) and swimming. I personally have never had problems exercising in a binder, but some say it can be dangerous. It can definitely make you more short of breath than usual, though, since your ribs cannot fully expand. But I have asthma, so I don’t typically work out that hard anyway

No, sports bras are the best option. Over binding can cause long-term damage. I got top surgery almost three years ago and you can still see the deformity in the front my rib cage/ sternum from the band of bras and binders over the years.