In the spirit of agnosticism, here's my attempt at trying to incorporate good points from both sides of this issue!
1. Is the author's distinction correct? Does 'homophobia' involve any type of belief or action (e.g. simply saying that it is wrong) that goes against homosexuality? Or does it just involve "hatred and prejudice"?
Here are some definitions for 'homophobia':
1. irrational fear of, aversion to, or discrimination against homosexuality or gay people - Merriam-Webster
2. Homophobia, stigma (negative and usually unfair beliefs), and discrimination (unfairly treating a person or group of people) against gay, bisexual, and other men who have sex with men - Centers for Disease Control and Prevention
Keeping these definitions in mind, I would say that there's room for someone to be against homosexuality while not being homophobic. The most obvious example would be if someone had a reasonable basis to go against homosexuality. I can't imagine there being anything reasonable that goes against homosexuality entirely, but instead it would probably be something against certain aspects or expressions of the behavior, like being against same-sex marriage
while not being against homosexuality itself.
Another example I can think of is if the belief is unproven either way, like if someone believes that God wants marriage to be between opposite sex couples. Is that belief irrational? I wouldn't know either way without there being evidence either way. The only way I would be against such a belief is if it conflicted with the available body of scientific evidence for homosexuality OR if Christians acted on such beliefs in a harmful way. But if they keep it to themselves, then I can personally accept that as not being homophobic.
The alternative, is labelling any and every of opposition to homosexual behavior/expression as being "homophobia" and I think that is unreasonable and would lead to censoring, in effect.
2. Is it even possible to believe that homosexuality is wrong but not hate it or be prejudiced towards it?
I think it's possible. For instance, a Christian can believe that adultery is wrong but not hate adultery or adulterers. But oftentimes Christians don't show that. We find a hyperfocus on homosexuality with many of them trying to find anything negative with homosexuality. Why not also look at the positives of it?
* I'm willing to amend or abandon my view for a more reasonable one.