Personally, I am not so much into sports due to laziness rather than any fear of Shrimat! Although I do enjoy walking. I remember someone I know being told they shouldn't go swimming, even though they wanted to do it primarily for health reasons. A lot of this is fear based rubbish, not based on Gyan at all; more prudishness. My experience is also that the senior crew don't necessarily say that you shouldn't do this or that, but you will get sniped at behind your back and not respected.
I've been visiting in the UK recently and one place I stayed at, from a recommendation by a BK friend, was a retreat place which is open to all as a health retreat and vegetarian guest house by some BKs who seem to have a chilled out attitude to exercise, therapies etc. It was nice to stay somewhere where I felt comfortable eating the food, and with the attitude of those treating me, and spend some time with a loving and accepting spiritual approach.
They do all the BK routine stuff, but its in the background not in your face. You wouldnt know if you were staying for therapies or accommodation, although they do offer free meditation sessions in the evenings for guests who are staying for health treatments, as well as Yoga in the morning. I joined Avyakt Murli Murli if I felt up to it and not if I did not; it was relaxed.
They did a special deals as I was staying for a few days. They told me they'd sent an open invitation to centres in the UK offering BKs discounts, but they hadn't had much takeup. From discussions I had, they seem to be accepting to all shades of BK, ex-BK, etc. Anyhow, it's in Wales and it's called the Phoenix Retreat. It's not listed as a BK centre.