Here's my take:

The problem with talking about "objective" and "subjective" with respect to ethics (the terms that "realist" and "anti-realist" often get unpacked to) is that they mean different things to people with different intuitions. I don't think there actually is a "what most philosophers mean by the term" for them.

"Objective" either means:

1. not subjective, or
2. It exists regardless of whether you believe it exists

"Subjective" either means:

1. It is different for different people, or
2. not objective

So, some people go with definition 1, and some go with definition 2. Very few people go with both Objective[2] and Subjective[1] and recognize that they're not negations of one another.

So you have folks who think that different people have somewhat different utility functions, and therefore morality is subjective. And you have folks who think that a person's utility function doesn't go away when you stop believing in it, and therefore morality is objective. That they could both be true isn't considered within the realm of possibility, and folks on "both sides" don't realize they're talking past each other.