In the Star Wars universe Jedi use different colours of lightsabers. I have noticed blue, green and purple in Star Wars original and prequel trilogy (I heard there are more lightsaber colours too). And Sith use the red lightsabers. I do know why Sith lightsabers' are red. But why are Jedi's lightsabers of different colour and what significance or importance do they have? I heard some story about their out of universe reason but I am seeking for in-universe reason.
UPDATE: Disney canon:
As per "Ashoka" novel by E.K. Johnston (via ScreenRant), Sith red color is explained. No more synthetic crystals.
Kyber crystals choose Force users and present themselves to their desired owner, but dark siders don’t experience this same connection to the cystals. The only way the Sith and other dark side Force users can collect kyber crystals is by stealing them or plundering them off the bodies of their fallen foes. Even if a dark sider were to acquire a kyber crystal from a green or blue saber, the act of bending the crystal to their will in a new lightsaber will cause the crystal to “bleed,” turning it red.
First, some in-universe background (some of which you may know if you know "why red").
At the heart of every lightsaber there is a "Kyber Crystal"
The crystals concentrated energy in a unique manner and were attuned to the Force, resonating with it
In Star Wars universe, Kyber Crystals come in 2 distinct varieties: naturally harvested (of varying colors) and synthesized using the help from the Force (when Dark Side is used, it imbues them with red(dish) color, as your linked answer hopefully states).
For natural crystals, which color crystal you used depended on the era:
Old Republic era - ~4000 BBY (Before Battle of Yavin). No films/TV shows depict it:
Around 4000 BBY, lightsaber crystals were used to indicate a Jedi's chosen class. Blue indicated a Jedi Guardian, a Jedi who used the Force on a more physical level. Green indicated a Jedi Consular, a Jedi who preferred to reflect on the mysteries of the Force and fight the dark side at its heart. Yellow indicated a Jedi Sentinel, a Jedi who honed their skills in a balance of combat and scholarly pursuits. (source: Wookiepedia)
In later years (around Star Wars movies times) that has long stopped, and the colors were simply a Jedi's personal preference, or which crystal they managed to get; especially post-Empire-creation time when they became a great rarity.