What series are we talking about? I can find no reference to "Songs from Distant Earth". If we're talking about the "Homecoming" series which begins with
The Memory of Earth, I'd say it was
pretty indisputable that it was based on Mormonism. He even addresses Parson's concern but I'm not sure how mollified Parson will be since it's something quite distinct to be modelling yourself on Gibbon vs. trying to retell Mormonism. I don't know many Gibbonites who think the status of their souls rests on his accuracy. But I only scanned the verbose essay - I can't read him at all.
But it's my understanding that Alvin Maker and lots more are all based on Mormonism and even bits of it are in the Ender books. Basically, it informs everything he writes, just like AnyaKimlin says it does his/hers.
But I dislike even
Ender's Game (which I think is one of the "gaming" novels of all time, in Parson's sense rather than in Ender's) and
Speaker for the Dead and
Songmaster and what short fiction I've read and disliked it all before I became aware of his personal issues so this is just based on what I've picked up in passing and a quick web search.
---
I've been following this thread and have started to post on it myself but haven't been able to come up with a list that seemed on topic and correct. Basically, I'd say that two of the most influential works I've read have been (speaking of Gibbon) Asimov's
The Foundation Trilogy, which really got me reading SF and turned me into an SF fan as such. Also, I'd say Will and Ariel Durant's
The Story of Civilization. I didn't read the first (Oriental) of the 11 volumes and only scanned the last few when they got bogged down in excessive detail on France vs. everything else (and might have nodded through the very large
The Age of Faith), but I devoured the bulk of the 2nd-7th volumes (
The Life of Greece to
The Age of Reason Begins) and, whatever its scholarly merits with historical detail, the comprehensive cultural view was very powerful and helped inspire me to view things much more holistically and temporally and try to fill in a lot of gaps in my readings/awareness from Greece to America. This also made me much more interested in viewpoints like Hegel's and Spengler's which might not have been Durant's expectation.
I don't want to give too much credit to either of them in that I'd seen science fiction and perhaps read it without really knowing it and I was fascinated by 20th century military history even as a small child but the Asimov and Durant definitely mark entirely different levels.
But, after that, it becomes much harder to isolate one thing over another. So there's a likely two of the five.