They can hardly be celebrated for fighting on behalf of a nation which did not yet exist, in order to prevent its coming into existence. Or it would seem rather odd, were it so. Here in Canada, we naturally celebrate Loyalists, and in particular, those who resettled in the Canadas, as United Empire Loyalists. But this is for precisely the reason that the United States does not, after all.

I contest the proposition that the American Revolutionary War was the nation's first civil war on the simple basis that it was not yet a nation such as might have a civil war.

The goal in the Civil War was to reunite the country. I.e. get everyone to accept, think/feel that they're part of this unified State (in the sense of "country) called the USA.

To that end, it's politically useful to claim that Confederate casualties are "our" casualties. We're all Americans, both Northerners & Southerners, and so Federal casualties are American casualties, and Confederate casualties are American casualties, etc etc.

I think with the Revolutionary War there simply isn't a similarly pressing political imperative. Rather than unifying, we were trying to break away to form an entirely separate country. Hence it's more natural to teach future generations to think of loyalists as "traitors" who sided with a foreign country (like Tokyo Rose).

Another way to think about it is, post Civil War, there is a big chunk of territory where the majority of the population has Confederate sympathies/is seriously pissed at the US. So eventually they figure out they have to assuage their sentiments to improve loyalty & unity. With Revolutionary War loyalists, there isn't a big territory where they (the loyalists) are the majority and we (revolutionaries) are the conquerors trying to persuade them to accept our rule. If anything, we were like the insurgency trying to throw off a foreign occupying army. And we succeeded where revolutionary sympathies are strong enough to overwhelm loyalist sentiments & British forces, and fail where they're not (Canada). So in the territories we end up holding, we don't really have to worry about separatist sentiments being stronger. So the much "simpler" solution of "persuading" loyalists to move away (to Canada, say) is viable.

They weren't initially counted as American casualties of war. Memorial Day was started by African-Americans in the south who spruced up the graves of the Union dead, but was later co-opted as a general military holiday as years went by. This co-optation was part of a process of general sectional reconciliation that promoted the message that all soldiers in the civil war died honorably and that began to re-write the meaning of the Civil War itself into some sort of disagreement in which slavery and freedom were not really part of the war. If you want to really delve into this subject, Race and Reunion by David Blight is the seminal text...

There are some good answers here, but this lands rather firmly in my wheelhouse and I wanted to weigh in.

As with so many things, the answer to your question lies in Reconstruction after the Civil War. To get there, we have to look at the motivations of both Loyalists and Confederates.

During the American Revolution, a sizable part of the population of British North America took action to make sure that the colonies remained part of the British Empire. Being that the Patriots physically controlled most of country during the Revolution, tens of thousands of Loyalists fled to British lines, particularly New York City. When the British gave up trying to conquer the United States and recognized American independence, those Loyalists that had fled to the British generally chose to flee the country rather than try to go back to their homes. Since their goal was to remain under the protection of the British empire, this course of action let them achieve that goal at the expense of leaving their homes and property behind. Most Loyalist exiles resettled in Canada, but some also went to Jamaica, Britain's other Caribbean colonies, and Britain itself. In the decades after the war, some Loyalists moved back to the United States. However, much like those Loyalists that had never left, they tried to keep their heads down and generally stayed out of public life. Some migrated internally, heading west so as to escape their unpopular actions during the war.

During the Civil War, Confederates fought to break off the South from the United States. When the Southern rebellion was finally crushed, the South and its people were reincorporated into the society and political body of the United States. Save for the very few Confederates that resettled overseas, they did not have the opportunity or inclination to flee the country like Loyalists did. Being that they stuck around, loyal Unionists and defeated Confederates had to find a way to coexist with each other. Most Southern whites wanted a return to normalcy as soon as possible - a state that they assumed meant the continued subservience and inequality of African-Americans, even if they did have to formally end slavery. Some Southern whites, of course, were violent white supremacists, who violently resisted any efforts to educate blacks, encourage their economic independence, or include them in the political process. This latter group, most famously embodied in the Ku Klux Klan, made the occupation of the South between 1865 and 1877 a bloody affair that exhausted the patience of Northerners that also wanted to put the human and financial cost of military operations behind them. Whites looking for reconciliation, both North and South, bonded over the shared experience of loss during the Civil War. So long as no one talked about the causes of the war, people could commiserate about the pain of losing sons and husbands. Veterans groups followed a similar track, focusing on the experience of military service and surviving combat. This pattern - shared celebration of military service, no talk about the cause of the war, and no black voices in the conversation - continued well into the 20th century. The 50th and 75th anniversaries of Gettysburg were officially treated as opportunities for white vets to hug and shake hands and focus on the good parts of what President Woodrow Wilson called "a quarrel forgotten." This narrative still dominates the way we talk about the Civil War, and Confederate veterans, even those that committed war crimes, are still honored by a number of Southern governments.

Sources:

Maya Jasanoff, Liberty's Exiles

Alan Taylor, The Civil War of 1812

David Blight, Race and Reunion