chances are, they’d think you’re a Marxist or someone old-fashioned in their speech…
This isn't a good thing; it's a result of a concerted effort to make people think Marxism is old and irrelevant.
I really dislike the notion that we should stop using the term 'bourgeoisie' just because of the pop notion that it's an outdated word and that nobody knows how to spell it.
Yes, the English language is constantly evolving and terms fall out of use, but as they do so the language doesn't just reflect the dominant thought patterns but reinforces them. English has a high chance to remain the most popular global lingua franca even after Western hegemony falls, and the evolution of the language will remain a battle ground.
There is slow progress in people learning that liberalism means liberty for markets and not for people, but most people still think it means liberation of individuals, genders and minorities. The fastest way to 'liberate' someone from that error is to get them understanding the class conflict, and the term 'bourgeoisie' is still relevant to that.
And then they kiss