You might be interested in an answer I just wrote on here: https://www.reddit.com/r/AskHistorians/comments/orfdb1/what_events_or_social_sentiments_lead_to_the/ I wrote on the origins of Western homophobia, but unfortunately not so much on the legal questions. My point was still that it was mainly the medical community that functioned as a major driving force behind what is now known as homophobia. Also I wrote about how our current views of what it was like to be gay 50, 100, 200 years ago tend to skew heavily towards the negative. Not that it isn't based on truth, but those stories are much more well known than stories of queer joy and happy protoqueer marriages.

The law enforcement in Europe generally speaking became much more interested in actively chasing homosexual people only during 20th century. In 1885 the British Parliament prohibited "gross indecency" or "buggery", meaning sexual acts between two men could be prosecuted even without "proof". Before that, proof that "sodomy" had taken place was required for people to be punished for it. The famous court case against "Stella and Fanny" had even fallen through since prosecution was unable to proof that either person had engaged in same-sex relations. This was in 1871, which was well into Edward Carpenter's lifetime. He probably would have read about the case in newspapers and might have even followed it closely - Stella and Fanny's court case was quite the spectacle for readers at the time.

Stella and Fanny were arrested due to "crossdressing laws", since they were AMAB individuals who were clocked on the street while wearing women's clothing. They had been indiscreet in public, and the police had had their eyes on them for a long time before they were finaly arrested. Stella and Fanny were then prosecuted of "conspiring to commit sodomy". Oftentimes the pair have been described as gay men who were drag queens, but we can't really rule out the possibility of them being trans women. Stella and Fanny both confessed to appearing in public in women's clothing, and they were bound over for two years, but not convicted to two years of hard labour, which would have been the punishment for "conspiring to commit sodomy". Their case was a key factor in the 1885 change - had there not been a requirement for undisputable proof, the two might have been convicted. Also, if Fanny and Stella had been arrested in, say, 1953 the outcome would probably have been very different. And by that I mean they likely would have ended up in prison or at the very least received a hefty fine. The 1950s saw an unforeseen spike in the mass arrests of gay men and people assumed to be gay men in particular.

Many people made no secret of their queerness and lived quite openly, and yet they never faced charges. In my opinion it is a historical fallacy that gay people were not able to have long term relationships - clearly this is not the case. So called "companionships" were relatively common even well before the 19th century, especially among upper class women. An extremely well known example is queen Christina of Sweden, who lived in a long-term partnership with countess Ebba Sparre, who Christina lovingly called her "bedfellow". Companionships are often seen as exclusive to women, but men also engaged in them. There are many interpretations as to what these companionships exactly encompassed, but many historians myself included believe they functioned as same-sex unions for protoqueer people. For example Anne Lister, a british landowner and diarist, who is often dubbed as "the first modern lesbian" lived in such a companionship with her partner Ann Walker. They themselves considered their relationship to be a marriage after they took a communion together in 1834. Of course same-sex relations between women were not illegal in Britain, but in my eyes this still serves the purpose of demonstrating my point. Also: these companionships weren't illegal - or how is one going to stop people from voluntarily living with each other as "friends"? Especially when during the 19th century ways of supervising people were pretty nonexistent.

Also note that this was a few years before Edward Carpenter was even born, but my point is that gay people have always been able to find ways to live together with their long term partners, even quite openly, and they were left alone by law enforcement. I see no reason to believe that lower middle class and working class people wouldn't have had "companions" as well, but known examples tend to focus on upper class people due to the source material that has been left behind. It is far easier for historians to study a queer landowner who wrote extensive diaries than a queer pig farmer who never even learned to write their own name.

To my understanding, Edward Carpenter lived in a companionship at least with George Merrill. The two became partners in 1893 and lived together for the rest of their lives. My opinion is that they both were likely protected by Carpenter's higher status as an upper middle class author, as well as Carpenter's previous partners. And I also believe that maybe they didn't do anything that anyone would have deemed that dangerous or disturbing. Even working class queer people and queer people who lived in rural locations were oftentimes left alone unless they committed some other crime or angered someone in other ways.

Also, as you can see from my other answer I linked here, the concept of homosexuality was very new when Edward Carpenter was alive. He himself talked about "Uranianism", which was one early name for gay men in particular. In his case, sodomy wasn't apparently proven in his young adulthood, and he and his partner were in a legal, albeit unrecognized, partnership. The words homosexuality and heterosexuality were coined by Karl-Maria Kertbeny in 1868. Even then and for quite some time after that, scientific texts on the matter were published in Latin in order to obscure "sexual details" from the public. So it is also quite likely that many people still thought of sodomy or buggery as the crime instead of homosexuality in itself. And sodomy had to be proven, or strongly assumed. Also, many people disagreed and didn't think there was anything wrong with same-sex relations, or didn't care.

Law enforcement also generally tended to be more lenient with rich and upper middle class people, with exceptions - like Oscar Wilde - of course. Even Stella and Fanny were both brought up in upper middle class families, and it has been suspected that the British criminal court wilfully ignored their "offense" in order to avoid convicting two people of relative wealth and status. He might have been a radical thinker, but did he actually commit any actions that would have branded him as dangerous? There were many people at the time who advocated for queer rights, women's rights, and socialism - many of them were friends with Carpenter, like Havelock and Edith Ellis and Olive Schreiner. In Germany, Magnus Hirschfeld was a very well known queer rights advocate and gay himself, but he didn't land in prison either despite being very outspoken against Germany's sodomy laws. He even escaped Germany in 1933 mostly because he was Jewish and an academic, so Nazi Germany wasn't the place to be for him.

TLDR for this answer would probably be that it was easier to be gay in the 19th century than some people generally seem to think it was, and mass arrests and huge raids to known gay cruising spots, bars and cafés became much more common only during the 20th century. Of course it cannot be ruled out that these didn't happen at all in the 19th century, but many areas just didn't that actively enforce sodomy laws yet. It was much more in the 20th century, when the terms homosexuality and heterosexuality had become much more established, and homosexuals were actively classified as perverse and defective somehow.

//e: fixed some language mistakes. Not a native English speaker, sorry about those!