Yorick, you have to accept people are comfortable with differing levels of nudity in changing rooms etc.
No, you need to accept that communal showers and changing rooms are for showering and changing, and this will involve nudity. If you don't like it, don't use them. But you can't dictate to others what to do.
Myself and my peers hated the enforced nudity for schools showers after PE.
I am sorry to hear this, but it is nothing to do with paying patrons using leisure centres.
Yes, other countries have different cultural norms, however you cannot just enforce a new culture onto children.
I haven't said anything about other cultures, but anyway. It is perfectly normal to be naked in a communal shower and changing room. I was briefly naked in one just this morning. Nobody ran screaming (although perhaps they should have done).
If it is vital that the club use the facility, then yes, they do need to do something to put minds at rest.
If they want exclusive use of the facilities, they must come to an arrangement with the centre. If for any reason they don't, they must abide by the centre's rules if they wish to stay there. And the centre's rules are that in this time, other people are allowed to use the sauna, showers and changing rooms.
As it is, your issues around nudity are not anyone else's problem, least of all a man who is using the leisure centre as he frequently does. If you have issues, seek therapy, but the world at large does not have to change to adapt to what you personally find comfortable. If you do not like communal changing rooms, don't use them.