Greek mythology and how it became a irrelevant religion?

They adopted Christianity in the times around Constantine.
A later emperor, Julian the Apostate, was educated in Athens and still believed in the old Greek gods. He attempted to relive interest in them by giving long boring speeches in public places in Constantinople, it didn't work of course.

Unlike Christianity, Greek mythology was not made into a law wherein the penalty for not believing in it was death.

The official polytheism of Greco-Roman culture had started to seem rather stale by the 1st century, which is why people in those regions were susceptible to various eastern mystery cults that seemed to offer more spiritual sustenance. Christianity was one of these. Early Christian missionaries (like St. Paul) were very effective at establishing Christian congregations in Greek-speaking regions, and the religion became popular enough that by the early 4th century, the Emperor Constantine declared it an officially tolerated faith. Later, it became THE religion of the Roman Empire, which comprised Greece and Greek-speaking regions.

There were holdouts among polytheists for some time, but ultimately, it was politically and socially expedient to drop polytheism and adopt Christianity.

Early Christianity grew gradually in Rome and the Roman Empire from the 1st to 4th centuries, when it was legalized and, in its Nicene form became the state church of the Roman Empire with the Edict of Thessalonica of 380. Hellenistic polytheistic traditions (the Greek gods) survived in pockets of Greece throughout Late Antiquity, but eventually disappeared.

The Roman Emperor Theodosius ordered the temples closed and everyone to go to church in the 390s AD.

Simply because Zeus was not giving the people the necessary spiritual and enlightenment that the people were praying for............ Which means that Zeus became irrelevant to the majority of the Greek people...................

From my perspective (I'm greek), you know how Europian countries had mythology as their "religion"? You'll barely find any of them, as almost everyone is now what l call a traitor and to be honest, l've been one before and in a way, I still am. Now almost all of them are christians. Hope this helps :)

Belief systems live or die depending upon a number of factors. The most important is if the culture survives. Getting exterminated (before the age of the Internet remembering EVERYTHING) is a great way for a belief system to die, especially before the invention of writing. A whole tribes oral tradition could, and did, vanish when it's last inhabitant did. You are too busy trying to maintain your own tribe's set of traditions to be worrying about the next tribe over, unless one of the girls was extremely hot and letting her teach you led to some other things..

As the culture dies, so does its flexibility. Stories don't just appear, they grow organically. Like a song, oftentimes the story that was written down was the most current version of that story, changed so much from its origin even the original tellers wouldn't recognize it. There are a thousand things not written down in the myths that everyone in the culture absorbs as being a part of them, as necessary to them as the myths themselves. Stories tend to preserve the plot-points of a mythology, while real-life introduces innumerable things that become harder to maintain when the culture dies.

And even if you aren't exterminated, losing a culture war is a really great way to make people not believe that their Gods are worth keeping alive. Of course, zealots and small pockets of faithful do help keep the myth at least culturally present, enough so that its germ of comfort can find fertile ground in someone else. Most people, sad to say, believe in winning. If Zeus (Greek culture) is winning, Zeus it is. Zeus gets replaced by God...Zeus is dead, long live God. Also, new cultures tend to be pretty zealous in making sure old Gods can't grow in the new soil. Your gods give your life meaning and justification: why risk that by allowing some other God to take up roost? And Christianity found that making religion an either/or situation in the era of writing meant that it really could kill belief systems simply by destroying its incentives and history (ask the Native American tribes that were assimilated.) Again, people are pragmatic and Gods are like sports teams. Yeah, Oakland may be really upset if/when the Raiders leave but give it 100 years and a different team/sport moves in, the Jerseys will be just another relic bought from the NFL store. When, for instance, was the last time you heard anyone crying about the Akron Pros?

One last question to consider: what constitutes a mythology? I mean, actual mythologies evolve due to the dynamic nature of the culture itself. Gods past become Gods present, so what happens when you are what's left? Hermes really isn't worth talking to if he looks down at the cellphone in your hand and goes "Forsooth, what magic is this? Athena, ye must stop and take a selfie with me." And that moment is truly when a belief system dies... when the Gods become so frozen, so ossified, so petrified and captured in time, they cannot grow. When there are no new stories to tell, there is little need to tell the old ones.

Mostly they were converted into Christianity.

Search on google "ysee helenism"

It is partly a case of merging! when more powerful cults etc appear they with their leaders eradicated often with violence worship of other deities, when the mighty Christianity appeared, its controlling leaders merged other traditional observances, for instance, Christmas was not to do with Christ but only as an added veneer, over the Saturnalia festivities of the 17th Dec ( drinking and giving of gifts) and Mithraism Festivities of Sun birth Worship 25 Dec and Isis who held a similar date 24th Dec for enticing back Osiris, it is a mishmash to allow people to have and enjoy their desired festivities, whilst cloaking it in a Christianesque manner that it appeased all, Nearly!.

Lol

Romans 11:33 New International Version
Oh, the depth of the riches of the wisdom and knowledge of God! How unsearchable his judgments, and his paths beyond tracing out!

Zeus in the temple proves Jesus Christ is Lord

Same way Christianity became irrelevant. It's called rational thought.

Many characters of mythology came about to explain natural events that ancients did not understand such as Zeus, god of thunder. They did not know how weather conditions created this roar so they created a god to attribute it to. Look up the meaning of myth. As time went on and we started understanding these events mythology became less relevant.