@Allie Jayne I agree that there is a difference. The impersonators were engaged in accurately mimicking a celebrity in every way for entertainment. Drag shows are often as you describe with over-the-top costumes and makeup, and there is a lot of confusion between what is done for entertainment and what is done for gender expression.
I have not visited my parents since my transition and it would not surprise me if they think my appearance now aligns with drag. I send pictures of me doing "Lori things" like metal detecting and rockhounding, which they know I do, but my appearance is slightly different. I'm wearing the same wide-brimmed hat but my hair is long. Hormones have changed my face and breasts and no more full beard. I ease them into how I look daily so that they can see that I am not wearing formal gowns and extreme eye makeup while gold panning.
We can't change the world's perceptions, but we can change the perceptions of individuals. Get enough of that going and the world changes on its own.