Is there a way to delete people from your friends list when they haven't been active in months?

Yes. Go into Social > Friends > Friendlist, then at the bottom right you will see 3 icons that look like little people. One has a "+" next to it, one a "-" and one is like a crossing out symbol.

The + will add friends if you have their player number.

The - will remove people from your list (click it and then select the players you want to remove from your list).

The crossing out will show the list of other players/Sultans you have blocked (actually blocking them is done by clicking on their avatar/icon > "Others" tab at the bottom right of the screen > and then choose how you want them blocked and make a brief report.