I'm stunned that the writer thought that the solution is to set up both a regular registry and a cash registry -- never even discussing the many good reasons that cash registries are Just Not Done and conflating some communities' customs (of cash being the traditional gift and/or dollar dances and the like) with cash registries. I feel sorry for the HCs who are going to follow this advice and be considered crass and mercenary.
It's customary to give a gift when you are invited to and especially if you attend a wedding. But it isn't an admission fee. HCs aren't entitled to gifts at all, much less to gifts of their choosing, whether that means cash only or believing that their guests are required to buy them gifts for which they've registered. Requesting cash is not only tacky, it's insulting: "There is nothing you could choose that could possibly mean anything to us, so just fork over some dough." [ETA: I mean requesting without having been asked directly by someone; if someone asks you, or better yet asks an attendant or relative, what you'd prefer, it's okay then to say that you/they are saving up for XYZ and leave it at that. That's not the same as giving out that information unsolicited. If you think it is the same, just leaving out a silly inefficiency, then ask yourself if you'd feel the same about a friend who answered your question what they'd like for their birthday as you would if they handed you a wish list without your having asked.]
If people give you gifts you don't want or don't like, then you deal with them the same as you would an unwanted birthday, graduation, or holiday gift -- exchange, donate, regift, sell, toss, or keep. And thank the giver. You aren't entitled to anything at all, let alone anything in particular. I don't know why some HCs don't realize how ugly it sounds when they even indirectly indicate that they are thinking otherwise.