Left and right almost have no meaning these days.
Never did. Left and Right originate in whether or not you sat on the left or right side of the president in the National Assembly during the French Revolution, the right side supported the King, and the left side were against the king and supported revolution.
If we were to use the 18th century understanding of left and right, it would mean reformists/revolutionaries and monarchists, respectively. So you can take this to mean, rightists support the status quo, and leftists want change. By this understanding, you could actually classify both the modern extreme right and extreme left as leftists, because they oppose the status quo of liberalism, while neo-cons and boomercrats are the only rightists in the country.
This is of course a bit asinine, because the meanings have changed, but this illustrates my point that it never had a solid meaning in the first place. Right wing doesn't mean blood and soil populist nationalists, go back 150 years, and those people would have been seen as leftists with an off-color agenda. On that same note, the Nazis and Fascists actually slot into the leftist category as it used to be understood, as they opposed the status quo.
That being said, you might have noticed that I actually use left and right in my own unhinged political ranting, because it's useful terminology given how people today have used it to self-categorize themselves. When I say right-wing, you know that means somewhere between Hitler (Ironically a leftist by the old meaning) and Sarah Palin, and when I say leftist you know that means somewhere between Stalin (Ironically a rightist by the old meaning) and Jimmy Carter, but this self-identified left and right spectrum can more or less be boiled down to "Are you racist and do you support the capitalist model?" Answer yes to both, you're based, answer no to both, you're woke, answer yes to one but not the other, you're a respectable moderate.