u/OldPersonName gave a very good answer about what the Cyrus Cylinder actually is, and why that isn't a charter of human rights. What I want to comment on is why the Cyrus Cylinder is, officially, the first charter of human rights. according to the United Nations.

The claim goes back to the last Shah of Iran, Mohammad Reza Pahlavi. After the 1953 Iranian coup failed, it was not immediately clear whether the Shah or his Prime Ministers' would be the real power in Iran, but Mohammad Reza intended to strengthen his own position. This involved crackdowns, intervention in the legislature, courting foreign interests, and the formation of an authoritarian monarchy. It also included a dramatic series of domestic reforms to modernize the country, known collectively as the White Revolution.

Most of the changes to government policy, infrastructure, education, etc. are not relevant to the Cyrus Cylinder. However, the general policy of secularization and the Shah's growing reputation as an authoritarian are crucial. To bring the country more in line with the social expectations of the West, both the Communist bloc and the NATO allies, the Muhammad Reza lifted religious prohibitions, such as allowing non-Muslims to take their oath of office on their only holy books instead of the Quran. More generally, he was trying to deemphasize the importance of Islam to Iranian culture, both to appeal to foreign supporters and to break the domestic power of the clergy. In the long run, this was obviously unsuccessful and led to the 1979 Islamic Revolution. In the short run, it was wildly successful and did exactly as intended.

To support this secularism, the Shah began appealing to Iran's pre-Islamic past, but it was also used to downplay the Shah's authoritarian policies. This was a conscious part of the White Revolution from the start. Mohammad Reza Shah formally announced the White Revolution by writing a book - maybe more of a manifesto - by the same name, published in 1963. The first chapter of the The White Revolution, contains the very first documented reference to the Cyrus Cylinder as a human rights document.

The famous document of Cyrus, which is one of the most brilliant manifestations of the rights of freedom and justice in human history began according to this charter. For the first time, the right to freedom of opinion and other human rights, as far as it is concerned Cyrus, were given. For the first time, this would be given to all the peoples of the imperial nations: freedom from plunder and looting, which was the accepted method of conquest. Slavery was prevented, and since then it has almost always been so in this country: a shelter and refuge for all members of minorities of any kind, of ethnicity and religion.

What's very interesting, from a historiographic perspective, is that the idea of the Cyrus Cylinder as a human rights document appears fully formed in the first documented reference. Mohammad Reza Shah almost certainly formulated its use in The White Revolution in preparation for his larger plans to highlight pre-Islamic history and the Iranian monarchy in advance. However, that doesn't explain where the idea came from or why he chose a document that so clearly doesn't say any of the things claimed in The White Revolution.

The answer lies in the history of the physical cylinder itself. Excavated in 1879, the first translations were published almost immediately, but cylinder itself was heavily damaged. A large chunk from one side, conveniently the end of the inscription rather than some of the middle, was missing. This initial discovery is "Fragment A."

Whether it was broken off while buried or by the excavators themselves, this missing section, called "Fragment B," was actually dug up in 1879 as well, but languished in obscurity as one of hundreds of inscribed fragments in the British Museum for decades. The text was translated and published in 1920, but only identified as the missing piece of the Cylinder in 1970. So from 1879-1970, the last ten lines of the Cyrus Cylinder were a mystery.

Today, there is a fake translation of the Cyrus Cylinder, or more accurately a fake translation of Fragment B grafted to the real translation of Fragment A, which pops up occasionally online. The fake translation is fairly consistent and clearly translated from another language into English, most likely Persian. There isn't much academic interest in that sort of hoax, so nobody really knows where it came from. However, it does very accurately reflect the claims made by the Shah and does fit in neatly to the gap left by Fragment B. That has led the few scholars who do comment on it to think it originated in Iran sometime in the last Shah's reign. Whether it was invented by the Pahlavi regime, someone who supported it, or circulated before 1963 and actually inspired the use of the Cylinder in The White Revolution, we'll probably never know.

As part of Mohammad Reza Shah's Celebration of the 2,500th Anniversary of the Founding of the Persian Empire (going off of Cyrus' conquest of Babylon in 539 to get a nice round number), the Shah's sister presented the UN Secretary General with a copy of the Cyrus Cylinder. The official gift was given as a copy of "The Edict of Cyrus," and the princess "said that 'the heritage of Cyrus was the heritage of human understanding, tolerance, courage, compassion and, above all, human liberty,"' according to the official UN report from 1971.

That report could just as easily have been written by one of the Shah's own propagandists for all the historical accuracy it provides. The official UN statements regarding the Cylinder, in 1971 and ever since, essentially repeat the Shah's statements from The White Revolution and the 2,500th Anniversary event despite the entirely different content of the document they discuss.

I'd be pretty wary of describing anything so ancient as liberal or conservative outside of the most anodyne dictionary definitions available, but I think by most definitions the answer is no. I suspect you're thinking of some myths about the inscription; that it abolishes slavery, does not impose his rule on conquered lands, etc. Those would be strikingly anachronistic and, sure enough, it doesn't say anything of the sort and nothing like that happened.
The cylinder is in many ways a very standard Babylonian type of artifact, intentionally designed to be very familiar to its Mesopotamian audience. From its design to the contents of its inscription. It was likely written as a way to assure the newly conquered Babylonian elite that no, things weren't going to change drastically and Cyrus was content to work with their existing social and religious institutions (which is, if you want to use the dictionary definition, kind of conservative!).

It paints the last king of Babylon, Nabonidus, as an impious unworthy king, not properly reverential to the Babylonian's chief god Marduk, and not carrying out his kingly duties. This wasn't a hard argument to make; it appears Nabonidus was pretty unpopular for just those reasons. Among other perceived failures he had spent a decade away from Babylon, during which time the important new year's festival couldn't occur. The king's presence was required for the festival which involved days of feasting and celebration, and the god Marduk himself (in the form of the statue kept in the inner chambers of the temple in Babylon) would make an appearance. It was a big deal. Cyrus appears to have exploited Nabonidus' unpopularity both to take over Babylon (relatively) easily and then to boost his own popularity.

As the cylinder tells it Marduk chose a successor, Cyrus, and brought him to Babylon to heroically depose Nabonidus and set everything right. The cylinder talks about Cyrus returning images and restoring sanctuaries throughout the land. This may just be plain slander - most cities had a resident god (in the form of a statue, like Marduk at Babylon) and Nabonidus appears to have brought them to Babylon for safe-keeping in anticipation of an attack. Cyrus paints that as yet another affront to the gods from Nabonidus and takes credit for returning them from Babylon (never mind that they were there in the first place to protect them from him!). Then he discusses building projects which is pretty much Mesopotamian royal inscription 101.

What about one of his most famous acts - ending the Babylonian exile and letting the Jews return to Jerusalem? This is attributed to him in the Bible (as the chosen of Yahweh, very similar to his role as Marduk's chosen in the Cyrus Cylinder), though evidence of any actual work on the temple reconstruction isn't until a bit later, under Darius. This also wouldn't be too outside the norm of Mesopotamian culture - kings often performed a sweeping "benevolent" act on ascension, most famously relieving debts (a periodic necessity in the cutthroat financial world then). He likely wouldn't have singled out the Jews for restoration, but as they were only 50 years removed there was still a strong memory of their homeland in their culture so many of them returned and wrote about it.