Elon Musk isn't right wing, he is a businessman that understands some balance needs to be brought back.
To be fair, when it comes to economy related issues, such as tax rate, wages, environment protection etc, right wing policy
generally favors business people.
I can't imagine people running a business AND agree that a large portion of business gain would be taken away by the government via tax. Or agree on policy that increases wages/energy price which reduces business revenue. This kind of policy is fundamentally putting social equality on a higher priority than economic growth, and it can hurt the benefit of a business.
So it is entirely understandable that a businessman is right leaning due to their role in the society.
However, one can be right leaning and still choose to use reasons and logic instead of relying on emotions when it comes to promoting their political ideology.
Supporting one side is perfectly fine. Propaganda is not though.