Why should anything be closed to them because they are black? some things are, either in fact or as perception.
Well, we could start with Augusta National ! Though that's an extreme example, and has changed a bit,joking aside the general perception is that golf is not an African American game. Here it is the same for black people. Golf was alway so, and may still be. Even Tiger Woods doesn't see himself as African-American , his ancestry being decidedly mixed.The old pros were often caddies who graduated to being pros, but black caddies didn't.
But it applies to class as much as to race here. Few working class people see themselves as polo players, however much money they have, and the typical golf club is a veritable haven for middle-class men with the Hyacinth Bucket attitude. A 'priceless' example:When I took one of the crew to play at Monaco Golf Club and he told the Secretary, who asked which club we belonged to before permitting us to play, that he belonged to an artisan's golf club, you could see the rolling eyes and hear the sigh from the other side of the room! I don't think golf here is so very much different. And tennis is still like that, by and large.
In all those circumstances, it's hardly surprising that black children don't see some games as 'for them'.