Your question is bit hard to answer since you do not specify to what nation or at least an area it pertains so I will focus on two areas. France and Prussia.

However, if you are interested about homosexuality in 19th century Britain, this lovely answer by u/smrzj should give you a general overview of homosexuality 'climate' at the time. https://www.reddit.com/r/AskHistorians/comments/os82zm/ive_been_reading_about_edward_carpenter_the_19th/

As for the claim about gay people being burned at stake until 19th century, it is not wrong. While not very common, since at the end of the 18th century there was a shift towards more leniency towards sodomy in Europe, there is an account of 7 parisian 'sodomites' being burned at stake between 1714 and 1783. However 5 of them also committed other crimes such as rape and murder.

The two remaining appear to be a case from 1750. Bruno Lenoir and Jean Didot who burned at the stake for what seems to be nothing more than having sex in January of that year, were unlucky in one thing. According to contemporary sources they were workers, had no connection to a people of privilege and they were made example of.

Interestingly enough, in 1772 the rather (in)famous Marquis de Sade was to be burned at the stake for sodomy along with his manservant. Both fled and were tried in absentia and in the end also burned in absentia... using an effigy.

Elsewhere, in 1730 a Prussian man was burned at stake. A decade later Frederick (by then not yet Great) ascends the throne. Why is that important? Frederick has himself almost certainly been gay.

In 1746 Frederick suspended the death penalty for sodomy in Prussia, recommending military labor as an alternative punishment, as well as a visit from a preacher.

In 1794 (when Frederick is already Great but alas no longer alive) Prussia officially reduces the punishment for sodomy from death by burning to imprisonment for a year or more, whipping, and banishment.

Sources: Homosexuality and Civilization, Louis Crompton

Homosexuality in Modern France, Jeffrey Merrick

I suggest you take a peek at an answer I wrote earlier on western homophobia: https://www.reddit.com/r/AskHistorians/comments/orfdb1/what_events_or_social_sentiments_lead_to_the/. The list u/Antiquarianism posted here might also prove interesting and useful to you: https://old.reddit.com/r/AskHistorians/comments/k0tufn/it_seems_to_me_that_throughout_much_of_ancient/ge849t4/.

This is indeed a difficult question to answer, since the original statement is so broad and generalized. My focus is on European queer history, so my understanding is affected by this, and in this answer I will be speaking of different European countries. My general short answer to this question is, however, both yes and no. You are very right to find the statement dubious, because that's absolutely what it is. It's a generalization that contains multiple historical fallacies, and in my opinion is also rooted in homophobia. To be frank, the statement displays no real historical value or knowledge about queer history generally speaking.

If we are to take the statement literally, then technically, yes, some gay people were indeed burned at the stake or given the capital punishment before the 19th century. My old answer I gave the link to gives some insight into the general terms of "sodomy", but to put it shortly, sodomy did not exclusively refer to same-sex relations. In European context sodomy meant all sexuality that was deemed "unholy", such as extramarital relations, anal sex, oral sex, masturbation, child and animal abuse, and so forth. So we can't be really certain as to what it specifically meant that someone was called a "sodomite".

The earliest example of two men being specifically prosecuted for "sodomy" meaning same-sex relation I can think of from the top of my head is from my native country, Finland. There are probably some earlier ones and other examples, but this came to my mind immediately. In 1665 the stablehands Heikki Pekanpoika and Heikki Mikonpoika from Taivassalo clergy house received the capital punishment for "sinful sodomy". They were executed by axe on a cliff known as the "cliff of tears" in their home village of Taivassalo in southwest Finland. The only remaining primary source on them, however, is only a brief account from the Turku court of appeals. They were given the sentence of beheading and burning the remains, but I didn't find out whether they were burned as well. Beheading by axe was the most common method of capital punishment in the kingdom of Sweden, which Finland was a part of at the time of this event. So, no: at least these men were not burned at stake for being gay, nor was there a special kind of punishment that was used for gay people specifically. Even when punishments were given out, they were in the realm of "normal" punishments for the time. From 1800s onwards increasingly imprisonment and fines were the main form of punishment for same-sex sexual relations.

What happens to the statement if we don't take it literally? It loses even more meaning. Let's assume that the person in question means that before the 1800s gay people were actively persecuted. Maybe they mean that queer people were forced to live miserable, closeted lives, since being queer was perceived as so wrong and sinful. The reason why I personally would answer "not really", to this claim, is that the statement in itself contains many historical fallacies we need to explore. First of all I assume that the person who wrote the statement assumes that the attitudes get exponentially more lenient over time, and places a major shift in attitudes at the 19th century. Generally the assumption seems to be that the more time passes, the better the world becomes and the easier it is for different minorities to exist. This is not the case here: generally speaking the law enforcement only became interested in actively chasing people who were homosexuals during the 20th century, and even that saw it's highest point during the 1950s. The differences between even different decades of the 20th century are staggering.

I, for one, think that in many ways it was significantly easier to be gay during the 19th than during the 20th century. It was only during the 1930s that psychoanalysts and sexologists actively labeled homosexual people as perverse - before that, it was debated more hotly. Sodomy laws that referred to same-sex relations more specifically started to pop up all over Europe during the 19th century as well, in place of the older, more vague ones. As I have already written in my previous answers around this topic, my belief is that the more medicalized and pathologized understanding that developed over the course of several decades in the late 19th and early 20th centuries affected how homosexuality was perceived. And the end result was that it was perceived as significantly more problematic than before.

In my previous answer I also talked about how source material we have available tends to skew towards the negative. I don't want to repeat myself too much here, but the point is that for much of European history we only know of the queer people that came into contact with law enforcement somehow, or otherwise left traces of themselves.

We would probably have no knowledge of Heikki Pekanpoika and Heikki Mikonpoika had they not come into contact with someone who disapproved, or if they had been of a higher status than they were. Also, maybe Heikki and Heikki did something else to anger someone? Maybe they didn't do their work properly, maybe they got in a fight with someone. Or maybe the fact that their employer was a literal priest had something to do with it. We don't know the details here, but I can only assume that there are many instances where the two Heikkis could have been very able to live together as companions and herd sheep or something. As stablehands they were most likely illiterate and unable to write, so we actually know nothing of their lives and what events lead to their execution. It's also a documented and known fact that people of higher status were tried and punished with more leniency, and even not prosecuted at all. Had Heikki and Heikki been noblemen or royalty, they would probably have been seen as "companions".

In the memory archive in my home town there are, however, loads of narratives of protoqueer people from similar backgrounds as Heikki and Heikki, who were loved and accepted in their communities as themselves. "They just were like that", or "this man lived with his close friend for decades" are common narratives that can be found, if we look for them. These narratives directly contradict the statement we are discussing.

It's also a matter of interpretation. Some people might outright refuse to see queer people in history, or do so unknowingly. Sometimes it is thought that it was always so very difficult to be queer, that queer people outright stopped existing somehow. Or that they even didn't exist before the coinage of relevant terms, which is an absurd claim at best and harmful at worst. Other reason as to why I think the statement is homophobic, is that that is often given as an excuse as to why queer history does not need to be discussed or taught to people.

And what about earlier points in history? For example Ancient Greece is notorious for having understandings of sexuality that is innately very, very different from later ones. A recent study from Finland, again, revealed the grave findings of an iron age nobleperson or a local ruler, who was most likely intersex and visibly queer, since the objects placed in their grave reflected multiple different gender roles. This person was respected and held a position of power, so again: no sign of burning at stake here. Or if we want to discuss the contemporaries of Heikki and Heikki, how about queen Christina of Sweden and her companion, countess Ebba Sparre? These are only a couple of short examples that directly contradict the original statement, and I assure there are many more to be found.

To sum it up, the statement is an overgeneralization, that is not to be taken literally by any means, and the truth is actually far more complex. Before the later half of the 19th century homosexual people were not actively persecuted for homosexuality itself, even though for much of history same-sex relations were considered a crime of some sort. Not everybody agreed nor did everybody care about the laws, and queer people were also able to coexist with straight people happily and peacefully.