Will deleting a request after accepting it lower opinion?

Yes, and it will lower opinion a lot. (The exact numbers may differ slightly between versions, but when you cancel a favor from the journal, it will lower opinion a lot more than if you say "No" in the first place.)

The following information was verified in The Escapists version 1.37 on Steam.

• Saying "Maybe" to a favor does nothing
• Saying "No" to a favor will lower opinion (-5)
• Saying "Yes", but later canceling from the journal will lower opinion a lot (-15)

(Reportedly, in some early versions of the game, cancelling a favor was buggy. If you said "Yes" to a task for Aaron that involved taking an item from Zeke, canceling from the journal should have lowered opinion for Aaron, but actually lowered opinion for Zeke. This is no longer a problem in the current version of the game.)

https://steamcommunity.com/app/298630/discussions/0/35222218796843647/

There is more information about how to raise or lower opinion on the following page:

http://theescapists.wikia.com/wiki/Stats