Safari Captcha

Ah. In that case, close Safari by swiping up from the bottom to show all open apps. Swipe left or right to Safari, the slide it up and off the top of the screen.

Next, open Settings > Safari and tap Clear History and Website Data.

Try Safari now and see if that does it.

It's all websites, …

That's a new one on me. I've never heard of such a thing. Something quite goofy is going on then.

Try resetting Safari. The fastest way to do that is to shut the browser down. Open your user account (Command+Shift+U). If you don't see the Library folder, press Command+J and check the box to show it. You'll only need to do this once. Close the options panel.

Open the Library folder of your user account. Move the folder Safari to the desktop. Launch Safari. It should appear as if you've never used it before. Try going to a few sites to see if the issue with captchas is gone.

Neither Safari or any other web browsers prompts you for captchas. The site you visit does. You'll need to contact the site owners and ask them why their site prompts for a captcha every time you visit.