How do I disable the pop-up blocker in Safari on iPhone?

Refer to Block pop-up ads and windows in Safari - Apple Support.

To allow pop-ups, Settings > Apps > Safari > General > Block Pop-ups > disable.

A Safari Extension may be interfering with that setting, so to rule out that possibility investigate Extensions under that same setting. By default no Safari Extensions should be installed.

It may not be sufficient to "shut off" an Extension. Try removing it. No Safari Extensions should be installed unless you have a specific reason for installing it and you have familiarized yourself with its limitations.

Excerpted from Get extensions to customize Safari on iPhone - Apple Support:

Important: Check the extensions you have installed and make sure you’re familiar with what they do.

That Apple Support document also describes how to remove Safari Extensions.