I'd like to re-use the opening from WillRoss1's answer
(First off, I completely agree that "that sounds good/bad" has NOTHING to do with consonance or dissonance! I, for one, LOVE a good dissonance! But I digress...)
Consonance and dissonance are (mostly) objective, however they are not context-free.
The same chord can work as consonant in one piece of music and dissonant in another piece, but this different effect is not primarily due to subject-difference of the listener but object-difference of the musical context. (It can become subjective in the sense that a listener who hasn't had much exposure to the genre yet may have not completely ingested the context and thus “pastes it over” with context from another genre, in which the chords would indeed have different consonance.)
To pick one concrete example, consider the use of the major 7th in classical music and in Jazz. In classical, this is generally a strong dissonance leading to resolution to the octave, whereas in Jazz a maj7 chord is a super-sweet consonant sound. Why? Well, both genres work completely different.
In classical music, melodic counterpoint rules supreme. If the main melody uses the ⅶ note, then this is not merely a choice of colour or artistic freedom but it has a purpose, to drive the piece forward, highlight a conflict that needs to be, well, resolved. The other voices are in this case aides who support the development in a well-organised way. In the simplest case this is implemented by resolving from a harmony with complex frequency ratios to one with simple frequency ratios.
In Jazz, this kind of thinking is kind of opposed to the underlying philosophy of individual freedom: the leading voice isn't some kind of dictator that demands the lowly servants to propel it to its goal. Rather, the accompaniment starts out and gives a sonic landscape, within which the main voice has a lot of space for individual expression. This actually tends to get somewhat easier with jazzy chords like the maj7, because there aren't too strongs points of gravity – the root is often played only by the bass, not doubled through multiple octaves as often done in classical music which would make a strong friction of nearby harmonics for the ⅶ note. At the same time, the maj7 chord has ample notes to make it a properly rich/warm/groovy sound, not just a distant hollow drone as might be found in some folk genres that also have individual freedom in the main melody focus.
Further points could be made here about e.g. the way modulations are used in both genres.
Now, you could certainly say that it is subjective – one person likes Jazz, they hear the maj7 as consonant. Another might like Bohlen-Pierce, they'll perceive the octave as dissonant.
Except, this is then simply a frame challenge. If you don't like a genre, then you'll not want to adapt your ears to the intended context. The music won't work for you – which is fine! But it doesn't mean that consonant and dissonant have different meaning for you in the context of that piece than for people who like that genre, rather it means that you're not in the context of that genre.
An even starker example of different context is Gamelan music, which has an utterly different harmonic/melodic/scalar structure from most other genres. But this isn't just because people from Bali hear intervals subjectively different, it is because this music is built around instruments to which the harmonic-series arguments simply don't apply, because they don't have integer overtones.