The first thing to discuss is how much the Illinoisans initially knew about Smith and the Mormons, and the answer is not a lot. They also didn’t know a lot about the 1838 Mormon-Missouri war. So as the various newspaper articles were transmitted and retransmitted there was a lot of skepticism about their veracity. Once the Mormon refugees started flowing over the Mississippi river in the winter of 1838-39 the Illinoisan opinion definitely swung the Mormons’ way. When two sides both claim to be victims but one side is showing up on your doorstep starving and wearing virtually nothing in the middle of winter, it’s easy to believe that they are the victims.

Once Missouri freed (allowed to escape) Smith and the other leaders, it only confirmed the Illinoisans in their beliefs. Even the Missouri papers were calling his first trial a sham, and for a couple years they did nothing to pursue or extradite the Mormon leaders, apparently content to just have them out of the state. To most Illinoisans it only confirmed that the Missourians were the aggressors. Given the sectionalism in the country at the time the Illinoisans were more than willing to give fellow Northerners the benefit of the doubt. Even later opponents like the Western World / Warsaw Signal Newspaper initially welcomed the Mormons to Illinois.

The Mormons also cultivated friendships, and made extravagant promises that politicians loved to hear. The Mormons were promising to turn the upper Mississippi into a trade and manufacturing hub. They promised to gather tens of thousands of hard workers and skilled tradesman that promised to make Commerce City / Nauvoo a rival to Chicago or Saint Louis. Which is exactly what everyone wanted to hear after the Panic of 1837 and in the middle of a recession. Illinois deeply needed more people, more trade, and more tax revenue. And the politicians were very willing to overlook some eccentricity and shady pasts to get it.

It also helped that the most ardent representative for Nauvoo and the Mormons, was himself (at the time) a non Mormon. John Bennett was their primary lobbyist in Springfield in 1840. And he routinely pointed out that the city charter would benefit believers and non-believers alike. Yes the town, he would argue, would have a distinctly Mormon character, but it wouldn’t be a Mormon town per se. In fact the original mayor was Bennett and included other non-Mormons like Daniel Wells. So by all appearances it was a secular body. It should be pointed out though that Bennett was baptized as a Mormon before he took office and Wells later became a Mormon apostle (and Mayor of Salt Lake City) so the city government wasn’t nearly as “secular” as it might have initially appeared. No one expected that Smith himself would become the mayor, chief justice, and general. He hadn’t ever held any office, and didn’t seem particularly interested in office prior to Nauvoo. So the idea that it’d be granting him anything in particular didn’t seem to occur to anyone.

Even the Nauvoo charter itself didn’t seem particularly unusual. It was largely based on the Springfield charter. The handful of unique characteristics didn’t seem particularly troubling to anyone at the time.

So now we come to the crux of your question. In the years leading up to Smith grabbing power there was no real reason to suspect it was going to happen. He hadn’t ever sought office before. Even his first office of city councilman wasn’t particularly prestigious.

When he did run for office, he wasn’t widely thought of a criminal within Illinois and hadn’t been convicted of anything or even legally accused of anything within Illinois. His previous legal problems in New York and Ohio were mostly unknown, and discounted when known. His treason trial in Missouri was seen as a miscarriage of justice. Plus Missouri’s abandonment of the claim appeared to have settled the matter.

It’s only after 1841 when Missouri finally decided to pursue extradition after all, that the extent and validity of Missouri’s claims came to be well known, along with his previous legal troubles. By that point however the Mormons had secured themselves a generous charter to manage affairs within Nauvoo, with little to no state oversight. When Smith was appointed mayor by the then almost entirely Mormon city council in 1842, the state had already ceded the power.

In short in Illinois when he was allowed power, he wasn’t considered a criminal. By the time he was considered a criminal, he already had the power.