“Is there something about sex that is inherently anti-woman?”
No, and literally no one who matters thinks so. (“Sex,” after all, is a very broad word that includes private, same-sex relations between women. So even the most radical of sex theorists cannot think that sex is inherently anti-woman since none of them argue that same-sex relations are inherently anti-woman.)
“I see the word “objectification” thrown around here without any qualification.”
What sort of qualifications are you looking for? Most people use the word assuming that those reading it have the basic intelligence to understand—or else research for themselves—what objectification is and that it always occurs in a context (and therefore logically cannot be an issue of inherency).
“There seems to be a near consensus that getting paid for doing anything that is considered sexual (posing for photos, dressing provocatively, etc) is necessarily harmful to women because it says that “women are only about sex”.”
This strikes me as an incredibly uncharitable way of reading such comments. The actual argument that some people have put forward is that the current social context makes it such that paid sex work contributes to underlying (that is, preexisting) essentialist notions about women, the role of women, and “women’s work.”
The same is true for the rather notorious arguments that PIV sex is always rape. These arguments use an operationalized, academic definition of rape that does not mean what most people mean by the word, and has to do with the PIV sex in the context of a particular sort of society. I don’t think these arguments are any good, but it certainly makes no sense to cite or critique them out of context just because it riles people up.
“But what jobs do not only value their employees for what they bring to the task they have been hired to do?”
Two points here. One, something that “happens to everyone” can be worse when it happens to a particular group.” Both the rich and the poor are forbidden to sleep under bridges or beg in the streets, but it clearly affects the two in vastly different ways. Two, this is why intersectional feminism is also concerned with the way in which social class affects one’s position in society. In any case, “I’ve got problems, too” is just classic derailment. It’s like going to a breast cancer rally and asking why no one’s talking about heart disease.
“There were people in debates during college that argued that any consensual sex between a man and woman was an act of oppression.”
No, they didn’t. They were arguing that there can be no such thing as consensual sex between a man and a woman in the current social context. We might think this is false, but let’s not straw man the argument. (And again, the principle of charity requires us to understand the argument this way even if the actual interlocutors you are thinking about did not voice their argument very well.)
“But does that mean that our heterosexuality and homosexuality is a product of our culture?”
If you’re really interested in this question, you might look into the work of Michel Foucault. His is the classic argument that sexual orientation is a product of culture (based in part on how many past cultures exhibit the same behaviors without having any predilection for our modern labels). And of course, it follows from the idea that gender—not sex!—is socially constructed that sexual orientation must be as well since the latter is parasitic on the former. So if one believes that gender is a construction, one must also believe that sexual orientation is constructed.
This isn’t to say that there haven’t always been people we would refer to as “men” who were only attracted to other people whom we would also refer to as “men,” but only that the essentialist approach to this—that is, making it part of someone’s identity—is constructed. Again, the arguments here are tricky. And it is not clear to me, at least, whether they work. But Foucault is nevertheless a good starting point if you’re interested in the question.
“Anyway, what is wrong with sex and sexuality?”
There’s nothing wrong with sex and sexuality. There’s a lot wrong with how it is used and conceived of in our current social context.