I think part of being a man is not caring what other men define your manliness as.
If you have an idea that “manning up” involves some change in machismo, I think that might be a little toxic. But, if in not caring that your behavior made other men think about, caused friction, and was then interpreted as machismo, that’s better in my book.
If you like the sense of machismo and that phrase helps you as an imaginative aid, then why not. But I think it can be more constructive if you can interpret manliness independent from machismo