Frequency response + or - 1 dB ??

Your hearing is so not +/- 1 db that that it won’t make any difference at all.  Buy the speaker with a reasonable +/- 3 or 4 db, and put your money into low distortion/high efficiency.  

Agreed, other aspects are also vital to good reproduction of music and sound. Seems there are questions about why frequency response accuracy is important.
Very simple. The aim of loudspeakers is to accurately reproduce sound (as recorded with the best of modern technology). For that, accurate frequency response must be a goal. Or am I mistaken?

@ptss 

It's a matter of preference and each recording itself has a different balance so the response of the speaker should be adjustable not fixed. But audiophiles dislike adding anything in the signal path. 

Would you please describe your current speaker syste, as well as any widely available commercial speaker you stan?

I don't have a current system. None that meet my standards can be found for a reasonable cost or perhaps even at any cost. 

The last speaker I had were called Green mountain audio chroma. However, they suffer from severe colorations which make them sound very cold. Additionally these speakers have zero baffle step compensation, in addition to poor bass response. There's no evidence they are time coherent either, only the manufacturers claim.