There a few ways in which a Northerner could be opposed to emancipation. I'm going to TRY to answer your question, and if I didn't really hit the mark please say so. This is a pretty multifaceted issue and I think each portion of the answer could probably be their own dissertation.

So, it was entirely possible for a northerner to be antislavery and also be racist. Jim Crow laws were passed in the north before the South because northerners were equally horrified at the prospect of a multiracial society. Of course, large Black populations existed in the South, but they were treated by law as property in almost all instances. Of course, there were some freedmen who lived in the South, but many states did not allow for free Black people to live in their state. Regardless, free Black folks in the South lived in a constant state of terror due to institutionalized violence and coercion intended to make live as difficult as possible for these people. This was a framework embedded in law and enforced by society, meaning laws and citizens worked together to make the life of a free Black person hellish. These conditions meant that freedmen often found themselves in northern communities. Many northerners were just as uncomfortable with a free Black family/individual living amongst them as a Southerner would've been, so emancipation alone (remember, citizenship guarantees as in the 14th Amendment don't come for a while at this point) would have been perceived as the start of a great exodus of formerly enslaved people to the north.

Many other white people felt like the Emancipation Proclamation missed the mark for one reason or another.

Lincoln was not exactly popular for most of his first term, in no small part because of action such as the suspension of Habeas Corpus and the institution of a draft. Many folks felt like their rights and lives were being stripped and that Lincoln could become a dictator - if they didn't already feel as though he was one. You can see Lincoln's relative unpopularity pretty well by looking into the results of the 1862 midterm election - in which Democrats managed to pick up several seats - and in the 1864 presidential election, which Lincoln had genuine fears of defeat. On that latter note, I suggest looking into breakdowns of voting trends between civilian voters and servicemen. Civilians broke - generally - for McClellan but the military vote - often occurring via mail on the front lines - went commandingly for Lincoln. Literature is interesting here, and if you'll allow me, I'd like to break it down a bit. There is an argument to be made here that a lot of the civilians felt like McClellan could negotiate some sort of end to the conflict, or that he would govern in a way more favorable to civilian interests. The literature isn't entirely sold on this point because the confederates were really struggling by the time of the '64 election, but that could have factored into a civilian voter's calculous - a softer approach could lead to peace negotiations instead of prolonging the conflict any further (as Lincoln's unconditional surrender policy would've called for) to avoid, say, a chance at being drafted again.

Sources:

The Fiery Trial by Eric Forner

Free Black Residency in Two Antebellum Virginia Counties: How the Laws Functioned by Ellen Eslinger

Lincoln, the Fall of Atlanta, and the 1864 Presidential Election by Robert Lowe