It means the speaker is being pretentious! "Aesthetically unacceptable" indeed! "Ugly" (without or without the 'plug' part) is what it means.
The word 'unacceptable' is itself 'unacceptable' and is one of my favourite hates. The OED doesn't list it (only 'unaccepted' and 'unacceptability' are listed ) People, usually officials, use it. Unacceptable to whom? They say it to avoid saying who it is who doesn't like 'it'. It's a way of shifting the blame.I am not finding it wrong, it isn't my boss, it isn't some committee. No, 'it' is wrong in itself, like one of the seven deadly sins, whatever 'it' is.The statement is unappealable and beyond criticism, like an absolute truth.
It's a dishonest construction.Either 'it' is unaccepted or it isn't. Having the tendency towards being 'not worth accepting, not likely to be accepted, not pleasing, not tolerable' [from the OED definition of 'acceptable'] is not what is meant.