Many reasons, but let me quote few people who actually declined the "honor":
"I get angry when I hear the word 'empire'; it reminds me of slavery, it reminds me of thousands of years of brutality, it reminds me of how my foremothers were raped and my forefathers brutalised."
"An OBE is what you get if you clean the toilets well at King's Cross station."
Quoting Michael Winner, a multimillionaire conservative, probably isn't your best line of argument :)
But seriously, these are both personal opinions, and the first one even seems to be working against your original assertion that the honour is meaningless.
All things considered, if you have an issue with the monarchy and the "aristocratic" government (not quite accurate, but there's a point there), that's completely valid. Rallying against an almost entirely unrelated honours system is way off-target, and I would imagine that abolishing it would do more harm than good.
I was asked - "why on earth shouldn't he accept the acknowledgement?" My reply is an attempt to provide a partial answer to that question, and is unrelated to the rest of the discussion. :)
"An OBE is what you get if you clean the toilets well at King's Cross station."
https://en.wikipedia.org/wiki/List_of_people_who_have_declin...