You can, of course, buy a domain, set up a website and not charge for memberships but choose who to admit and who not to admit. This is done when the profit is intended to come from sales to members after they join the site. There are free network sites that might be used for your purposes. Two examples of free membership sites are Group sites on MSN and groups on Yahoo. It costs nothing to set these sites up and there is no charge at all for a person to join. There are no paid administrators or moderators.
Each site sets its own rules for how to join and the code of conduct for the site. The site topics are many and varied. There are many support sites for those with health problems or concerns and for those who have suffered the loss of loved ones. There are sites for those who are passionate about crafts like quilting or woodworking. There are sites for those who love to travel. There are sites for different age groups from teens to seniors. The sites include chat software and a limited amount of space for posting pictures, documents and links per member. The free sites do not have such things as access to specialized data or lists. They dont give access to such things as music lessons.
Paid for membership sites are set up by businesses or individuals with the objective of making money by supplying hard to find information, access to specialized data or lists, or instruction in various fields. Membership sites are owned and operated by people who either own the sites or who are hired by the site owners to monitor and administer them. The topics for paid for membership sites are even more varied than the free sites and certainly more specialized.