I've read conflicting arguments over whether Chaucer was a Lollard or not and whether he presented his Parish Priest as one.
This is something the academic community has been going back and forth on for a few decades now, pretty fiercely from time to time (i.e., them's fightin' words). Terry Jones--yes, the Monty Python guy--wrote an entire book arguing that yes, he was, and it's very good and accessible reading if you're up for it. But he certainly doesn't get the final word on it.
In short, Chaucer was never officially accused or convicted of being a Lollard in any records that we know of. Of course, that doesn't mean he wasn't one, and there's a few reasons to debate it. First of all, Chaucer lived during the very beginnings of what would get branded Lollardy, around the time John Wyclif was still spreading his teaching. None of the "heretic scare" of the early 1400s had set in yet, and it was generally a much more intellectually open time than we give it credit for--this is the time when Chaucer's poetry can get popular, after all. Part of that is because the current king Richard II was turning a deaf ear to Thomas Arundel, the archbishop who would later open the floodgates to heretic-burnings, censoring texts, and a litany of other measures that did a lot to foster hostility toward religious dissent. Another thing to consider is something that's relatively new work in heretic studies: not all "Lollards" were Lollards. In other words, there were a lot of different people with a lot of opinions, many of them on public record, that were not what you would call orthodox, and for a very long time, scholars have stretched "Lollardy" as an umbrella term over them because the courts of the time did the same thing. However, not enough of those people had consistent enough views that you could really call them an organized heretical movement of any kind (though actual Lollards appreciated it). So, even though writers like Chaucer and Langland and Kempe were most definite outspoken critics of the clergy, that was a pretty common sentiment at the time. England was in upheaval at the time--in 1381, a huge insurrection of the commons surged into London trying to abolish serfdom and protest their exclusion from written records. Wyclif was turning the nobility against the clergy. So yes, characters like the Parish Priest can turn up representing what you might see as Lollard ideals, but they were largely just that--relatively common ideals that a lot of people held to different degrees.
Then 1399 happened. Richard II got deposed by the usurper Henry Bolingbroke (Henry IV, first of the Lancastrian kings). In a scrambling effort to make themselves look as legitimate as possible, the Lancastrians styled themselves as rigidly orthodox. Between the political turmoil of Henry IV's reign and the terrifyingly pious Henry V, Archbishop Arundel got his way, brought about the Constitutions of Oxford (academic censorship) and De Haeretico Comburendo (literally "of the burning of heretics), and it very quickly became very dangerous to have heterodox views.
Chaucer died just after the usurpation. Spoilers for Terry Jones's book: he thinks it was murder, and he thinks it was on Archbishop Arundel's orders. Chaucer died very suddenly (just after making a large down payment on a new home) with very little remark, even though he was still popular at the time of his death (and traveling around quite a bit). There's no indication that he was in poor health, so all in all, yes, he died under suspicious circumstances. He was also part of a circle of nobles called the "Lollard Knights." I know that sounds like pretty damning evidence, but it's worth noting that these men were more or less just a medieval book club, and a few of them were outspoken political protectors of Lollards. But Chaucer was connected to them, so it might make sense for someone like Arundel to target a popular, connected author with anticlerical feelings.
...but we don't have direct evidence that he was a Lollard, and (almost stepping out of history here) I think it's a stretch to say he might have been. Lollards are characterized by actively undermining clerical excess, and the kind of social critique we find in the Canterbury Tales isn't quite as heavy-handed. Many strict Lollards were also members of the nobility, as much as they tried to present themselves as the "voice of the people," which doesn't quite fit Chaucer's bill. It's clear that Chaucer poked at clerical corruption, but he doesn't seem to have the dogmatic objections Lollards did.
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