There is definitely objectification of both sexes.
I totally know what you mean about women being reduced to our looks. I'm having to get used to being treated as if I'm invisible in all sorts of social situations. And I'm far from ordinary looking - way taller and thinner than most women my age.
Objectification of women is much more visible than objectification of men, because women complain about it. Objectification of men is just as pernicious. We watch war movies and see scores of men gunned down by machine gun fire. We don't see them as people, simply as sort of toy soldiers.
So when a president tells us, "let's go invade some smaller country because we don't like their religion", the nation cheers him on, remembering those objectified men from our war movies and video games. Our legislature approves it by an 80-20 margin. It's only afterward when we learn the stories of our soldiers who came back maimed and about the family members of those who were killed that we wonder why we were so eager to play international bully.
Athletes (mostly males) are objectified. We've built a system where they do horrendous things to their bodies for our entertainment. We pay the 0.1% at the top ridiculous wages and required the other 99.9% to basically sacrifice the normality of their lives and the endurance of their bodies if they want a shot at that money. In many place status and popularity depend on being able to perform on an athletic field and the willingness to sacrifice body and time to achieve that performance.
Males are also financially objectified. If you don't or can't earn what society expects, you are less worthy.
Men are emotionally objectified. Men are allowed to display anger or grief, but are basically denied the full range of expression that women are permitted.
And men are violently objectified. Every living male has had, at some point, to defend his worthiness by fighting. My own father, a pacifist and the gentlest male I've ever known, encouraged my childhood male self to fight bullies when I was being picked on.
I've got to agree with FA. Being objectified sucks on both sides.