Are you asking if the average Chinese today can read a handwritten love letter from Confucius? Or if the average Chinese can sext with Confucius?

Reading text handwritten by Confucius could be difficult for some Chinese today if they aren't sufficiently educated since Chinese script has evolved over the centuries. Seal script (篆書 zhuànshū) was invented in the 800s and 700s BC and is probably what Confucius (500s BC) would have written. By the end of the Han Dynasty (200s AD), we already have script that the average Chinese today can definitely read. In fact, Chinese script in the Ming Dynasty (1368 - 1644) is basically the same as what is used today

As a result, reading something handwritten by Confucius would not be as easy as reading his YouTube comments. However, that presents a different challenge as well. Classical Chinese is quite different from modern, vernacular Chinese. The average person would struggle to understand Confucius speaking in the video, but reading the subtitles is doable with, again, sufficient education. In this case, there are cultural gaps that need to be bridged, much like there are if we were to read Shakespeare and Chaucer

Hello. Good question.

I've read that ancient Chinese such as that Confucius wrote are still mostly comprehensible in modern times, however the same cannot be said for other languages like English which is supposedly barely comprehensible only 500 years ago. Is this true for either Chinese or English?

It's not actually true of Chinese. At least, not without training, but then the same can be said of Chaucer. Chinese (using the term broadly here) has undergone considerable semantic shift on a wide range of lexical items, and the syntax of Classical Chinese has also changed significantly. One can learn the rules and the different meanings of words, but without some education you're not going to be able to just pick up a text and know what it says. This is aside from the very frequent allusions that are packed in most older texts, meaning you'd also have to know what those were referring to of you'd miss the metaphors/analogies.

To what degree have Chinese texts been translated and localized for modern audiences in the way that classical European and other areas of literature have?

To quite a high degree. I have in front of me my copy of 《老子章句解讀》, which is a quite well respected interpretation of Lao Zi's Daodejing. In it, you're presented with a verse-by-verse explanation of what's being said in the original. These sorts of interpretations are all over, and any book shop in China is going to sell dozens for each major classic work. This happens to be my favourite for Laozi, and the one we used in my grad program in China, but it's by no means the only one.

Anyone who can read Mandarin and wants to know about the Classics will have no difficulty finding books to explain the meanings and offer other helpful footnotes.

Would a modern Chinese person be able to understand Confucius' or Mencius' writings without any kind of intermediary dilution?

Nope, not generally.

Or is it similar to how Greek and Latin texts have been translated into English and other European languages?

"Translated" isn't the best word, since a lot of these texts are inherently vague, so having a side by side commentary is preferable. "Interpreted" is a better word (and coincidentally the same one we use for what might otherwise be called "translations" of the Qur'an)

How hard would it be able to understand Chinese writing from two thousand years ago compared to early Christian scriptures and literature?

This is hard to answer because, even assuming you're comparing a Modern Mandarin speaker and a Modern Hebrew speaker and giving them texts in Classical Chinese and Biblical Hebrew, I think it's not a fair comparison, considering Hebrew is more of a revived language. Someone like /u/gingerkid1234 will be able to address this better than I can, but my sense, as someone who'd taken a Biblical Hebrew class with a handful of speakers of Modern Hebrew, is that they're more similar than Mandarin to Classical Chinese is.

Putting that specific example aside, you should think of it more in terms of Mandarin = Modern Italian, Classical Chinese = Latin, but then on top of that, it's a really contrived form of Latin that doesn't reflect how anyone at the time was actually speaking. Imagine Latin that were highly poetic, included a lot of allusions to stories from Ancient Greece that people back then would recognise but aren't well known today, and that's getting closer to it. Granted Classical Latin didn't actually represent speech all that well either.

Does the fact that Chinese does not utilize an alphabet make it easier to understand historical documents than alphabetic languages?

It kind has an alphabet? What I mean by that is if you saw the character 圊 in writing, you'd have a damn good chance at knowing how it was pronounced, even if you didn't know it meant "toilet". However, yeah for the most part the fact that the pronunciation isn't as strictly encoded into the writing system means today we can see 圊 and just pronounce it the way it's said in Modern Mandarin, and no one really loses any sleep. Most people are reading the Classics with the Mandarin pronunciation running through their head. Most people won't know the historical pronunciations. Though if you want to know the classics well, you do need to know something about the historical differences, such as 王 as a noun having a different tone than 王 as a verb, which is an important distinction in a sentence of only 4 syllables.