My 8 yo hates football. He has dyspraxia. Fortunately neither DH nor I could give a shit about football, and for a child like DS, it's a horrendous sport to participate in. There's the ball control, anticipation of what is likely to happen and co-ordinating with other people. From being a toddler, he's been a ball-hog, and never really grasped sharing the ball to and fro. DS2 gets it. DS2 is a great influence on DS1 as there's often the sibling rivalry to not want to be trounced by his little brother, although there have been times that DS1 has watched DS2 swinging around in a playground, sighed and decided to scratch around the mud with a stick instead.
I get DS1 because I've been there. School sport was pointless as a form of exercise. The energetic bit was getting changed. The rest was institutionalised bullying by the people on school teams, standing around, being shouted at and trudging around after wayward balls. Fortunately outside school I danced and got into DoE and have become a fit, active adult because I don't have to do teams and I can do things on my own terms. I've gone from the wheezing kid at the back over a lap behind everyone else to running half marathons for pleasure (I suspect not living in a cloud of smokers has helped)
With DS, the same as a pp, we do swimming, karate and parkrun. Also cubs. Timing matters to us. DS can not cope with anything directly after school, although awkward timing of swimming lessons means we have to launch off to the pool. We have a fun splash session while we wait for DS2 before DS1's which in reality is a bit of bobbing around collecting floats.
I suspect DS is hypermobile and he is certainly sensory. He relaxes in very odd positions, and has recently complained about his knees when doing 5ks. I do wonder if a lot of his "toddler" tantrums when out were connected to discomfort when moving about (there were certainly a lot about clothes, changes of routine and sensory overload).
Other give aways about DS1 are his lack of table skills, general shuffling around, and appalling handwriting; holding a pencil is physically painful to him. He is socially and physically burned out after school and he needs gentle nudging, carefully selected activities, lots of bribery and listening to to be an active child.
It was crap being a girl who couldn't do team sports. It must be harder for boys in the face of tribe mentality, and DS1 gets that with his class. There's only 12 boys in the year group and most are on some kind of team. Fortunately there's enough Legoers and Minecrafters to be friends with.
If they do really want a social connection over football, you can encourage the geeky side of following a team and knowing stats. For DS, he's not as bad as he thinks he is, he's "just" anxious, overthinks and is risk adverse.
Being active is important, but pushing it is counter-productive. It needs to suit the child, be fun (e.g. pokemon go while walking the dog) and low-pressure (the beauty of parkrun is that it's not the rigid ranking that you get in a class and non-competitive).