While the Missouri compromise and increasing slave/abolitionist divisions flared up at the time Maine became a state, these weighty, national issues actually didn't have all that much to do with the referendum process itself. The referendum was decided based on locals attitudes towards Massachusetts and the laundry list of smaller concerns that went along with that. That said, Mainers were generally very anti slavery and detested the Missouri compromise.

The Maine statehood initiative began almost simultaneously with the formation of the United States. The first referendum on statehood was in 1792, so this was not a new issue and the concerns involved predated the more heated national disputes over slave states. Statehood was one of the defining political issues in Maine from the very beginning. The referendums always saw significant popular support, so the situation in 1819 was not unusual.

Maine was always in a very peculiar geographical position relative to Massachusetts - Maine residents living on the border with Canada would have needed to undertake a pretty arduous journey just to reach their government in the south. In the early stages of Maine's history that didn't matter as much because most settlement and economic activity was coastal, and the coastal trade in Maine did have strong and easy links with Boston.

But to pay off its debts and fund the new state, Massachusetts began to sell off public land in the interior of Maine, leading to a tremendous land rush in the late 1700s and early 1800s. The population of the state exploded. These interior settlers, mostly looking to claim land for farming or working in forestry, had very little connection to the distant government in Massachusetts. These inland farmers also identified strongly with Jeffersonian Republican politics and detested Massachusetts federalism.

The breaking point was the War of 1812. Maine felt abandoned and betrayed by Massachusetts after the state was essentially left defenseless to be invaded by the British in 1814. This caused other issues (like the extreme distance to reach Mass govt entities and courts, lumber laws, etc) to boil over and by 1819 the popular support for statehood was undeniable. While some Mainers did vote against it, the referendum was still 70/30 in favor of home rule. It wasn't really close.

Of those who opposed the referendum, almost all were in York, Lincoln, Cumberland, and Hancock counties. More broadly, support was mostly concentrated along the coast and to the south. The southern coastal region had more in common with Massachusetts, were closer to Massachusetts, and generally tended to be more politically plugged in and involved with Massachusetts Federalist politics. The coastal shipping interests in Maine also had more in common with the coastal shipping interests in Massachusetts than they did the inland population of Maine. It's not surprising that some support would be found there. But even so those counties still favored the split.

The actual sentiment towards the proposal was essentially the same as it had been for decades. Maine had favored self rule since the founding of the nation. The new Maine constitution was nearly unanimously ratified and attitudes towards statehood were strongly positive. The new constitution reflected Maine's priorities and differences from Massachusetts. It was a very Jeffersonian effort, with major distinctions like basing state house representation on population instead of wealth (as was still the case in Mass). Maine embraced a much more egalitarian approach to government with a focus on equal representation (by the standards of the day) and strong rights, especially in freedom of religion. The new state also jumped at the chance to utterly screw over the native tribes, who had many treaties with Massachusetts, in new and creative ways.

As far as the Missouri Compromise goes, it actually had little to do with the process and result in the state of Maine itself. Maine had passed the referendum and gotten a bill through the Mass legislature before the compromise happened, and ended up having basically no say in the process. It was one of the most strongly anti-slavery states in the Union, so there was opposition to Missouri and slave states in general. But that had little impact on the election or push for statehood.

This was mostly drawn from Banks' Maine Becomes a State: The Movement to Separate Maine from Massachusetts, 1785-1820.