But the console won't let me sign in unless I give it another email address and a phone number.

It used to but now it refuses, why is this?

For those connected experiences. Always online spamming love. 

It surely has a crush on you. 

phone number ????? never had that one lol....

let us know if you solve it.... it might be useful one day....

So no one knows what's wrong?
I don't want to give them another email address, nor do I want to give them my mobile or home phone number, but it's not letting me sign in unless I give it those things.

Click no or this one works. Something like that

Give them fake info?

There's no option to decline their request. There's only "press B to go back" pressing B signs you out.

As for putting fake details, the idea of the request is that I get an email or a text/call with a code to enter any time I sign in, using a fake one won't be helpful.

Xbox 360? They asked me for a second email ages ago. I just pressed the Home button and skipped it. Never asked me again.

This one keeps asking every time I try to sign in, if I press the home button it signs out or keeps me signed in but offline.

Which would be okay if I wasn't trying to sign in so I can download something.

Would you mind creating another email just for this? If that's not too hard/annoying to you, then you could just do that.