These were hot button issues because the reserve clause represented the old way in which owners of sports teams completely controlled their players while the idea of free agency was what the players wanted as a way to assert their independence and to make more money.
Before Curt Flood challenged the reserve clause, players could not move from team to team without the permission of the owner. This meant that the players essentially had no way to force owners to pay them commensurate to their worth. The owners would simply dictate what salaries the players would make and the players had not choice but to take them.
The reserve clause was a symbol of an older, more patriarchal America where authority was always obeyed. Free agency was and is a symbol of a more modern America where everyone pushes for their rights.