That depends largely on your perception of what a cowboy is.
If one is a left leaning urban or suburban raised individual, that knows nothing of people that live in the country (outside of what big media has told you) you might also think they are all rednecks that play the banjo and date their cousin. However if you are not one of them you should never use "the R word".
I know plenty of "cowboys" and they were raised "conservatively" with manners to be polite and respectful of others.
A lot of people are correcting you, Kimberly, and as someone born and raised in a rural area -- and as someone who has lived in southern and northern US states -- I say you are right.
Overall, people in the US don't view cowboys as "gentlemen". Sure, some are, but the ones that take up 4 parking spaces for their trucks, who are misogynistic toward women, who throw beer cans in their neighbors' yards, etc. are creating negative impressions and people remember the bad before the good.
As far as I know it's a pretty universal usage, with the cowboy definition being sort of a regional South American thing? I normally just use "vaquero" to mean cowboy, thus removing any ambiguity.
I've also heard cowboy as "gaucho" (though this feels decidedly Andean) or "charro" (though this sounds kinda rude and disparaging to me).
I'm not a native speaker, of course, so take this with a grain of salt!