What if you say no?

It's not really consent if declining affects your chances of getting credit or, worse, employment.

Yes it is, this is literally how credit works. You convince them you're credit worthy, they give you credit. If you don't like the particular information a credit company needs to trust you, then you try a different credit company.

I don't follow how declining a credit company would affect your employment, is there something I'm missing there?

Having credit is not optional in modern society.

In the US, where credit cards are notably popular, 70-72% of people have a credit card. In other countries, it is less than this.

Even if you don't have a credit card you may have a mortgage, or a car loan, or a business loan, or...

To have none of those things in the US you must be either very rich, very poor, or dependent on someone else who does.

Many people rent and buy cars with money they have saved. Some others, use public transportation. While many middle-class people take advantage of credit, it is not a requirement to participate in modern society. It is optional, in any normal sense of the word. Search "debt-free lifestyle" and you'll find blogs of many who advocate for living this way.

If this data is available to some parties, it will eventually be available for everyone interested. Especially when we are talking about Equifax, there should be no doubt.

You simply don't get approved for a credit card if you say no. They won't even accept your application without permission to pull your data.