Or an otherwise upper-class sport. The two sports I normally associate with rich country clubs are golf and tennis. Golf is obviously an upper-class sport because along with the care put into maintaining the huge course, there’s the clubs, the shoes, the balls, the clothes, the silly hats, all kinds of stuff that needs to be bought.
With tennis, though, all you really need is a raquet, a ball, and a net. Many other sports require more than that. Baseball, for example, is open to anyone, yet it needs a specialized field with all kinds of special equipment. Why is tennis typically a “rich people” sport?
A lot of the stuff you mention–shoes, balls, clothes–is just as necessary for tennis as for golf (exactly how necessary it is for either is up for debate). Good tennis racquets aren’t exactly cheap, either, and need to be restrung or replaced a lot more often than golf clubs. Then there’s court time–there may be free courts maintained by the park or school systems, but generally those owned by clubs are better maintained, and if you want to play in the winter you have to buy court time at an indoor place.
If you decide to get really into it, there’s the cost of doing club stuff, getting lessons and seeing a trainer, etc., not to mention the time commitment implicit in all of that.
So, while you can buy a couple rackets and smack the ball around a little bit in a school court, I’d say the situation is actually comparable to golf.