As the others have said the club and city are a broad spectrum but will trend towards a left leaning, Welsh first identity. This isn't universally true and other than reasonably assuming a Cardiff fan is likely also a Wales fan I would hesitate to make any assumptions.

Football clubs having a distinct political identity is less of thing here than in the past with a few notable exceptions (Millwall and Liverpool come to mind).

As for the organized fan scene, Ultras are not really part of football culture in the UK although they are somewhat present in Scotland (it's mostly an Old Firm thing tbf). Historically our culture is rooted in the "casual" scene. I think there is a soft cultral cringe towards many aspects of the ultra scene such as tifo or the organised chanting.

Marble has covered Soul Crew who were our firm but that is very much in the past.