Gonna have an Obi-Wan moment here and say yes, from certain points of view. I'd like to politely suggest that your assumption that Brundage was referring only to moral opposition to slavery was just that, an assumption (to be fair, it was somewhat implied by the language of the article).

The drawback of media articles like this is that they have quick statements and can't take time to fully unpack things. What Brundage said was true once properly contextualized. In short, a Union soldier might be eager to destroy slavery for several reasons, not just a moral repugnance.

1. By the election of 1860, the vast majority of white Northerners were anti-slavery, which is NOT the same thing as abolitionist. Most often, they opposed slavery on economic grounds as unfair labor competition and a threat to prosperous westward expansion. They were pretty damn racist, didn't want black Americans around them, but they also didn't like the idea of enslaving them. Still, they agreed that states had a right to legalize slavery if they wanted, meaning they couldn't dictate to the South. This antislavery mentality is what drove a lot of 1850s animosity between North and South, and got Lincoln elected in 1860.

2. The war was caused by slavery, but initial hostilities were sparked by the act of disunion, i.e. the South trying to secede. Most white Union soldiers in the early years of the war were fighting to keep the South in the Union, not abolish slavery. However, this changed over time.

3. As hostilities dragged on, more and more white Union soldiers were directly exposed to the realities of slavery, and this helped turn their opinion. It did not create an army of abolitionists, but it helped soldiers accept Lincoln's mounting insistence that slavery would be a necessary casualty of the war. Soldiers, over time, were increasingly eager to destroy slavery, but not necessarily out of concern for black Americans. Instead, it was a way to end southern oligarchies which might try to politically "enslave" them via the government, as well as a way to punish the South for the war it started. Further, slavery was widely seen as a misuse of labor and land which held back the United States from true prosperity. In other words, slavery could very much be considered an evil by Union soldiers without their regard for black lives.

4. Ta-Nehisi Coates also brings up a good point: we need to check our definitions. When we consider a question like this, are we only thinking about white Americans? Over 150,000 black Americans, many of them former slaves, served in the Union Army by war's end. It's safe to say that those soldiers were far more likely to fight in hopes of destroying slavery.

5. Finally we need to remember that even though the majority of soldiers did not fight out of direct moral opposition to the inhumane enslavement of black Americans, some still did. If people want to trot out the singular example of Lee when discussing reasons to fight the war, others can certainly bring out singular examples of their own.

Source used: Gary Gallagher, The Union War