We used to play 'Cowboys and Indians' all the time. (I was always chosen to be an Indian - no idea why!) And we watched westerns at the cinema very often.
I do try to live my life avoiding causing pain or unpleasantness, and if certain songs, cultural practices etc offend, embarrass or anger certain groups of folk, I'd stop.
But I sometimes think these 'woke' objectors are not deeply upset at all, just looking for an outlet for their activities.
Similar to those who complain about blackface Morris 'on behalf of' black people. Black people are perfectly capable of speaking up for themselves if they're truly offended.