A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
If i lost honor from an opponent and am ignoring honor requirements from my in clan personalities for the rest of the game and my opponent plays Respect http://imperialassembly.com/oracle/#cardid=10952,#hashid=e5fdaa8ba440ee8fa39b5eef093adfc7,#cardcount=2
Do i need to pay 2 extra gold for my men?
Respect doesn't care about you being able to ignore Honor Requirements or not, it just compares the Personality's Requirement with your Family Honor. If the comparison is negative for you, you have to pay 2 extra.
Note that using Respect wouldn't make much sense if you didn't ignore Honor Requirements somehow. If you didn't ignore them, you'd never have even the chance to Recruit those Personalities with HR higher than your Family Honor