Enable Two-factor authentication without being logged into an iOS/macOS device

The Apple ID I use for my developer account is separate from my personal Apple ID. All my devices are signed in with my personal Apple ID.

I was trying to set up Xcode on my machine, and when I went to sign in to my developer account, it told me I had to set up Two-factor authentication.

Upon going to the Apple website to do so, however, it told me I had to be logged in to the account from an iOS or macOS device to set it up, which I am not. So how can I use Two-factor authentication (presumably via a trusted phone number) with my developer Apple ID without being logged in to that Apple ID on a iOS/macOS device?

The linked MacRumors article discusses your exact concern and solution in detail:

• How to Set Up Two-Factor Authentication for Multiple Apple IDs on One Device

As of February 27, 2019, Apple is requiring that all Developer accounts with an Account Holder role be secured with two-factor authentication in order to ensure that only the account owner is able to sign into the account.

The requirement has caused some confusion among developers who have multiple Apple IDs, particularly those who use a dedicated Apple ID for their Developer account that is separate from their primary iCloud account used on their devices.

The solution to the problem requires you to login with your developer user account on a trusted device. This can be done by creating a new/temporary user account on a Mac, logging into iCloud with your developer Apple ID, activate Two-factor authentication when asked to and entering a phone number to receive text messages.

You can then proceed to setup an iOS device to receive verification codes without enabling other iCloud features. Go to Settings app → Passwords & Accounts and add a new iCloud account. After authenticating successfully, choose not to enable any of the iCloud features and save the account.

This way you can have a trusted device setup to receive Two-factor authentication codes without logging out of your primary iCloud account on your device.

You have to be logged in to that account so that you can receive the two-factor authentication codes. However, for a device to be trusted for an Apple ID, it does not have to be logged in as the primary Apple ID on the device/account. You can log in to many Apple IDs while keeping your existing Apple ID as primary. On iOS, go to Settings → Passwords & Accounts → Add Account → iCloud.

For anybody wondering if you can also enable 2-step verification without an actual IOS device. You can use the steps provided on this page