Well-read people pronounced it to be rubbish and vexatious at its core (8)
I believe the answer is:
literati
'well-read people pronounced it to be rubbish' is the definition.
I can't tell whether this definition defines the answer.
'vexatious at its core' is the wordplay.
'vexatious' becomes 'liter' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'its' becomes 'tis' (I've seen this before).
'core' says to take the centre.
The central letter of 'tis' is 'i'.
'liter'+'at'+'i'='LITERATI'
'and' is the link.
Can you help me to learn more?
(Other definitions for literati that I've seen before include "Bookish types" , "Learned, well-read people" , "they devour a lot" , "Learned people, men of letters" , "group of learned people" .)