I am not sure the examples you've given are male privilege.
Examples are male friends my own age (50) looking for relationships with much younger women
They are perfectly entitled to. IF they succeed, that means the younger women agreed to it! Women can do the same if they want. Look at the French president.
Men in very good careers, not having had to take career breaks for children
Women don't have to take career breaks for children either. Or indeed have them at all.
not being judged on their looks or weight
Men get judged too - balding, overweight, facial hair, not dressing correctly. Type of car they drive, etc.
being able to delay having children until they were 'ready', i.e.,40 plus
That's biology, not privilege! Male sperm DOES deteriorate, though they do have longer than women as a rule to procreate. You can hardly blame men for the menopause!
No negative connotations attached to being a single older male, not being called 'spinsters' or 'crazy cat lady' etc
I've heard eternal bachelors called all sorts "probably gay", "weirdo", "bet he's a strange one". Anyone who acts outside the norm gets it.
I'm also struck by how many traditionally 'male' professions are so much better paid than female ones. Why are certain jobs considered more 'important' in society?
No such thing as "male" and "female" professions any more. So if a female wants to be an engineer with the pay-packet that goes with it, go for it! Certain jobs have always been considered more "important" in society and a lot of "lowlier" jobs were indeed done by men. Think of the tradesmen, sewage worker, dustmen etc. Most of these jobs are done by men. I don't see many women fighting for the right to do those!
I am an older female with no children and never done the traditional female anything. I neither know nor care if I am seen as a "crazy old cat lady". Perhaps I'm too feminist to notice schoolyard name-calling or to be affected by it.