If someone clicks a frame and it redirects you to an external website, is there a way for the external website to know the user's FID without having to sign in with Warpcast?

Yes.

On frame's first page, user would need to press say a "Start" button. This calls the post_url on your server with the FID.

In response to this, the server will send back a new frame, with redirect button that has the target url appended with query param of ?fid=123

User then clicks this btn to get redirected

Casting /apoorv
Building🕵 impersonator.xyz
🟥 swiss-knife.xyz 
🔍 eip.tools
🖼️ framestore.xyz
🏗️ apoorv.xyz 

OK this is a really easy to understand explanation. Thank you!