According to the article it seems nobody really knows, and there is no evidence they were destroyed on purpose. So do you have some additional information?
But it then quotes another source that "the Greek Church authorities, supported by the Byzantine emperors, burnt eminent classical Greek poetry, including Sappho’s works, and replaced the burnt poems with those of Gregory of Nazianzus."
Now, there are no other sources that the author knows, and there is no any other source claiming something completely different. And knowing the general context, at that time there was no need to actually burn some works to prevent them to survive. As the books were not printed, somebody had to copy the book letter by letter. Therefore somebody must have "preferred her work disappearing (or at least not being saved)." The only thing we have to figure out, who that "somebody" could have been: effectively all the books that survived through these times were copied by the monks or for the religious rulers, and we also know quite well what their preferences were.
Therefore, the ending of the article: "Was it the flames of Sappho’s burning love that ultimately put her own work on the bonfire?" is very, very mean. It is virtually constructed to sound like blaming a victim.
If you've just casually read the article I'm not surprised that you may have missed that. That's what prompted me to speak in clear words, which is obviously considered "offensive" for some people here, even if the events happened more than 1000 years ago in the different context as today and we are only discussing that. I consider that absurd. But maybe that's the reason why the article author also made that inappropriate ending.
The apparently "offensive" sentences I've written here aren't different from the sentences from the bestseller works from 300 years ago. It's obviously not only progress that we witness in our times.
The only thing we are not 100% sure is if the book techically disappeared in flames. What's behind the disappearance is really clear. Moreover, we can consider how much we can trust that claim "the Greek Church authorities, supported by the Byzantine emperors, burnt eminent classical Greek poetry, including Sappho’s works, and replaced the burnt poems with those of Gregory of Nazianzus." It is the only specific claim we have, so it is must be treated as such.
It is not really clear to me, even after reading your comment. Can you spell it out? "Religious fundamentalism" is not in it self an explanation - why for example were Plato preserved and even venerated then?
https://blog.logos.com/2013/11/plato-christianity-church-fat...
Plato was definitely not somebody who wasn't to the taste of the Christians. And he can't be meaningfully compared with Sappho, who was obviously seen as a "pure" example of "incompatibility" just like some other antique traditions. Please see my other comments here for the context of the actual writing against female and male homosexuality by the earliest writer, Paul, in the very oldest texts of what later became the New Testament! Read the context there, (although I understand it can be hard as it will probably be greyed, hidden etc. even if these aspects are widely known among the researchers, for centuries) here I just quote:
"Romans 1:26-27 King James Version (KJV)
26 For this cause God gave them up unto vile affections: for even their women did change the natural use into that which is against nature:
27 And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompence of their error which was meet."
Once again, note that this is an older Christian text than the Gospels!
And again, regarding the connection to the Greek philosophy it's the Gospel of John (written later than Paul's Epistles and also later than other Gospels and the Acts) that starts with (in the original Greek) "In the beginning was the Logos, and the Logos was with God, and the Logos was God." (that's the correct translation of John 1:1):
https://en.wikipedia.org/wiki/Logos
"Despite the conventional translation as 'word'," ["Logos" was] "not used for a word in the grammatical sense; instead, the term lexis (λέξις) was used."