Would they?Merchants would certainly not see themselves as the equal of a logger or simple farm labourer, they'd see themselves as better. The same would be true of a craftsman like a blacksmith ot silvermsith when comparing themselves with an unskilled labourer.
What if they had developed a cultural view of themselves as a classless society - similar to modern America? Where classlessness is really a myth, but pretty much everyone considers themselves middle class.
A "classless" society with a modern rationale for that belief may be a modern phenomena, but something similar happened over a millennium ago with the spread of Islam. The Persian Empire, for example: while it still had a ruling class, a soldier class, etc. in the medieval period, it also had a very wide middle class that pretty much everyone else saw themselves as part of. And a prevailing belief that thanks to Islam, which had become the mainstream religion by the ninth century CE, all were equal. It wasn't nearly as stratified as European society of the time.
It doesn't really take a modern mindset to create that sort of "we're all equal" belief. Just a rationale that fits the culture. Probably some kind of revolution in the collective belief system would be necessary, but it doesn't have to be a primarily political revolution. Mass religious conversion could do it. Or, really, some influx of any kind of philosophy, as long as that philosophy promotes egalitarianism.