I get picky about word choices, and for me 'disdain' often nails what people mean when they reach for contempt.
Disdain carries that cool, dismissive quality — it’s less about loud hatred and more about looking down on someone or something as beneath notice. I use it when the emotion is precise: a mixture of superiority and refusal to engage. It works well in sentences like, 'She regarded the proposal with disdain,' because it implies judgment without necessarily implying violent feeling.
If you want to compare, 'loathing' and 'abhorrence' are hotter, heavier words; 'scorn' is sharper and more mocking. So if you want the most natural, versatile substitute for contempt that still suggests a moral or social distance rather than pure rage, I'd pick 'disdain.' It reads clean in narratives and fits both spoken and formal contexts, which is why I reach for it a lot when editing or writing dialogue.