80s (or earlier) sci-fi book, population relocated to a new planet long ago and is now split into wealthy Dome inhabitants and outsiders

You're describing "This Star Shall Abide" by Sylvia Engdahl, published 1972, UK title "Heritage of the Star". Two later books ("Beyond the Tomorrow Mountains" and "The Doors of the Universe") form a trilogy; all three were published in a single binding in 2000 as "Children of the Star".

Many spoilers lie below, only the biggest protected by spoiler tags.

The premise of the book was about a group of people that relocated to a new planet. The story begins long after the group had been on the planet for generations and the history of the relocation had blurred in the minds of population.

Noren grows up in a static, agricultural society that is dependent upon the benevolent dictatorship of the Scholars who live in the city. Radio communication, water supply, and purification of land for growing crops is only available through the Technicians sent out from the city.

At the beginning of the first book, Noren has no idea that he is in fact living in a "lost colony."

The population had ended up divided into groups - those within the Dome who had privilege, control, wealth and who processed 'the potentially poisonous food' for the rest of the population.

The Scholars and Technicians of the city are respected, sometimes revered, and occasionally (but rarely) reviled.

Only land that has been prepared using Machines from the city can be used for planting. Only grain grown from Prepared land can be used to feed chickens which will be eaten. Only water from rain cisterns or from piped from the city can be drunk or washed with. These are the strictures given by the Prophecy, which (among other things) claims that the Mother Star will appear in the sky at a set date in the future, and at that time the city shall be made available to all.

Later, we learn that these prohibitions have to do with

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The remaining masses lived outside of the Dome.

The majority of the society is a peaceful, homogeneous, agricultural society. There is no innovation and some severe limitations, for it is a society of stone, with no wood or metal (no axles, no hoe handles, primitive digging implements) but the majority of the people are happy or content.

Noren, who is a very intelligent man and perhaps excessively literal, rejects the Prophecy of the Mother Star and feels that the Knowledge contained in the city is everyone's right. He is frustrated by the limited tools, but has no resources to make better - metal is only found in Machines from the City. He becomes a rebel, goes to the City and denounces a Scholar, is captured and brought into the City for a series of interrogations and, later, lessons about the world he lives in.

Generations later, people only knew of their mythology and that when 'the evening star or sun' finally came in the sky all people across the plant would get access to the secrets in the dome.

The people are promised that in the time when the Mother Star, a new star, appears in the sky, they will be given Machines, and Knowledge, and become Technicians and Scholars themselves. The Prophecy both lays out the strictures on how life must currently be lived, but also lays out hope of a better life.

Unusually for such a document, the appearance of the Mother Star is clearly and precisely dated; it is not a vague apocalyptic reference.

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The reveal in the end as I recall was that the mythology that sounded so controlling, fabricated and designed to enslave actually had a scientific basis.

True.

and

By the end of the first book, Noren has learned that many of these things which he doubted were based quite firmly in fact.

Books two and three are about what Noren goes on to do, and how he works to fulfill the Prophecy - not, perhaps, exactly as it was expected to be, but in the end the City is opened to all.