See the email, a newspaper article about it, and commentary, at Pharyngula, Leiter, and What's Wrong With the World.
The relevant paragraphs of the email seem to be these:
But the more significant problem has to do with the fact that the consent criterion is not related in any way to the NATURE of the act itself. This is where Natural Moral Law (NML) objects. NML says that Morality must be a response to REALITY. In other words, sexual acts are only appropriate for people who are complementary, not the same. How do we know this? By looking at REALITY. Men and women are complementary in their anatomy, physiology, and psychology. Men and women are not interchangeable. So, a moral sexual act has to be between persons that are fitted for that act. Consent is important but there is more than consent needed.
One example applicable to homosexual acts illustrates the problem. To the best of my knowledge, in a sexual relationship between two men, one of them tends to act as the "woman" while the other acts as the "man." In this scenario, homosexual men have been known to engage in certain types of actions for which their bodies are not fitted. I don't want to be too graphic so I won't go into details but a physician has told me that these acts are deleterious to the health of one or possibly both of the men. Yet, if the morality of the act is judged only by mutual consent, then there are clearly homosexual acts which are injurious to their health but which are consented to. Why are they injurious? Because they violate the meaning, structure, and (sometimes) health of the human body.
I don't see how the claim that this is hate speech could be supported. It's ignorant, offensive, and poorly thought-out, for sure. But not really hate speech, as far as I understand what the legal definition of hate speech is supposed to be.
But on the other hand, I would be very uncomfortable teaching the material Howell claims is the official position of the Catholic Church in the manner Howell presents it, out of a fear of being unfair to the Catholic Church. This line of "argument" is barely coherent, really stupid, factually incorrect about how homosexual relationships are often conducted, and relies crucially on basic logical mistakes.* The fact that there are "philosophers" who think this is a reasonable and fair statement of a cogent argument for a true ethical conclusion is disturbing.
If this email is representative of Howell's classroom behavior, it would be much easier to sustain a charge of incompetence than a charge of hate-speech. The second paragraph quoted above does not represent a single, unified line of thought. It's a mishmash of points about how homosexual relationships work, what "fits" with what, and some stuff about consent that goes unexplained. If I had written that paragraph and then showed it to someone, I'd be pretty embarrassed.
As another example, Howell's email raises this as the key problem for utilitarianism:
One [problem] is that to judge the best outcome can be very subjective [sic]. What may be judged good for the pregnant woman may not be good for the baby. What may be judged good for the about-to-cheat-husband may not good for his wife or his children.
Now, there is a clear sense in which the possibility of the inherent subjectivity of value is a problem for utilitarians. But all contemporary utilitarians know about this (though Bentham and Mill seem to be somewhat oblivious to it), and all contemporary utilitarians have adopted a set of value-theoretic assumptions that rule out such a simple-minded objection. The utilitarian acknowledges that (playing along with Howell's example) the mother may have an interest in obtaining an abortion, and that this may not be good for the baby. The idea that the utilitarian is now simply stuck is stunningly ignorant. It is a defining characteristic of utilitarianism is that there is a way to compare the interests of the various parties, and that the right thing is what would be best, with everyone's interests taken into account and where everyone counts as one and nobody counts as more than one. The mere fact that an action might be good for one person and not good for somebody else is not an objection to utilitarianism, and anyone who thinks it is should not be allowed in front of an ethics class.
And the News-Gazette article also contains this passage (slightly snipped), focusing on what he says about academic freedom:
"My responsibility on teaching a class on Catholicism is to teach what the Catholic Church teaches," Howell said. "I have always made it very, very clear to my students they are never required to believe what I'm teaching and they'll never be judged on that." ...
"I tell my students I am a practicing Catholic, so I believe the things I'm teaching," he said. "It's not a violation of academic freedom to advocate a position, if one does it as an appeal on rational grounds and it's pertinent to the subject."
There's some tension here. For one thing, it's a little hard to square his contention that he doesn't require his students to believe what he's teaching with the way he characterizes himself as an "advocate" for religious and ethical positions that he lets his students know he holds. When I teach controversial ethical or religious material, I specifically do not tell my students which side of the controversy I stand on. For one thing, my classes are not about me; my classes are about the views and the arguments. For another thing, if they don't know which side you're on, it's harder for them to accuse you of being unfair to the other side. Howell says he is merely trying to hold them responsible for knowing what Natural Moral Law says about the moral status of homosexual sex acts and why, and is specifically not trying to get them to see things his way—it won't affect their grades, anyway. But he simultaneously lets them know that he accepts NML, believes what it says about homosexual sex acts, endorses those arguments, and is serving as an advocate for that position. If you do that, you are guaranteed to have some confused students on your hands. Maybe he wasn't proselytizing, but he was skating a fine line that would be invisible to someone without a lot of intellectual sophistication.
Secondly, it is not obvious to me that academic freedom gives us the freedom to literally advocate controversial religious and/or ethical views in the classroom. Formulating the views is fine. Stating and explaining the arguments that proponents of those views give is unquestionably our job. Showing how someone would offer a counterargument is obviously part of the job, too. But I don't think of my job as involving the advocation of my own ethical or religious views.
* For example, Howell writes, "NML says that Morality must be a response to REALITY. In other words, sexual acts are only appropriate for people who are complementary, not the same." In my own writing, I restrict the expression 'in other words' for situations in which the words that come after it are literally a restatement of the content that precedes it. In other words, I use that expression to indicate that I am clarifying, and that I am not adding on to, extrapolating, or inferring. That's not what Howell is doing here. Howell is drawing an inference, and this inference is valid only on the assumption that a bunch of controversial auxiliary premises are true.
Howell also writes that "Men and women are not interchangeable. So, a moral sexual act has to be between persons that are fitted for that act." This is a non sequitur. It is not a sequitur at all.