As someone who's known about this game for a long time?

No clue. They might hint at continuity, but it's hard to tell.

One thing is that they appear in specific endings, not in an order. Also, there are also two more hair colors, meaning that there are 7 in total.

1 is the one shown in the true ending flashback. It's dark brown.

2 is the one that appears in Anna's endings. It's a dark reddish-brown.

3 is shown in Bryce's endings, as well as the post-credits scene of Lorem's Good ending. It's a light reddish-brown.

4 is the one shown in Remy's endings. It's a dirty blonde.

5 appears in Lorem's endings. It's strawberry blonde.

6 appears in Adine's bad ending. It's blonde, but with a tint of red.

7 is the one shown in the true ending and while doing the secret ending. It's regular blonde.

There's also the secret files-only CG of Reza and Izumi plotting together. Due to the lighting, it's hard to tell if it's 2, 3, or 5.

Now, what's the canon reason to the different hair colors? It's hard to say. They might be a result of natural timeline variance. Or maybe she dyes it arbitrarily.

One interesting factor, though: in Anna's bad ending, you give Izumi a cheek scar by hitting her with Reza's gun. From that point on, her scar never disappears, no matter what ending you do. It seems like more than just information can be carried through timelines.

Thanks for all the information, I actually only noticed this after extracting all the files and looking through them (thanks for that btw)
Cannot believe I didn't notice it throughout my two full playthroughs.

Personally I think it could either mean it's just a variation in the timeline continuity or it's her hair becoming bleached due to repeated portal uses, like her pigments fading.

They must be different iteractions of Izumi that come from different timelines. As seen in the true ending she had also to kill her double in the past each time she travels back, and she replaces the Izumi of some of timelines. We know she does sometimes with the Remy ending, and probably did many other times that aren't know to us..
Other times Izumi dies in some timelines and in the next we meet another herself.
In any case, seems she has a way to prevent the memory loss caused by death/time travel, and probably is the necklace: the purpose is "send back in time" her memories each time she dies.

The way she remembers things is probably just System, who is able to monitor the Player's activities. She also has enough experience to have even better recall than the player.

Of course, I wouldn't be surprised if the necklace will tie into the sequel's time-travel mechanic, if it has one.