Is there a way to work out safely? Complete air replacement and surface disinfection. That can realistically only be done outdoors.
As a club kid who refuses to grow up, I bring my professional club lights and a mobile DJ speaker to the park to dance with a friend. She has a much harder time coping with isolation and it helps her. It is a system for events of 50-100 people, so it is loud enough to mimic the experience. I would actually be OK with us both wearing Bluetooth headphones like my JBL BT Reflect Mini, which are robust enough to wear while dancing and doing crazy head moves, but a club speaker sounds different because of the reverb from the surrounding environment.
We still wear masks despite not touching and being completely outdoors. We do not need to according to laws of physics, but not doing so would contribute to the attitude that masks are optional. They are not optional. As much as I trust my friend and she trusts me, there is no way to know with certainty we can not infect each other after a day of interaction with other people.
One way to setup a safe workout would be to use the gym's parking lot and set it up with gym flooring and 10x10' canopies. Portable patio heaters would keep the person warm when warm weather ends. They are expensive, but one way to solve that would be to setup a solar array and use electric heaters.
Another friend who is a Zumba instructor is hosting classes in a park's parking lot. That works for her and her students and it is safe.