Color identity can be different things:
1. The beliefs and personality and philosophy of the character
2. The mechancial color identity of a planeswalker card
3. The magic the character uses
And in regards to each:
1. Every actual human being has some personality aspects from all 5 colors. That's how the colors are concepted. That means that any especially well-rounded human character, and probably quite a lot of non-human ones, will sometimes dip into every color. But most characters (and probably most real people) strongly favor 1-3 core colors over the others. So keep in mind what your characters' core values and personality traits are, but don't worry if they don't hit every single trait in a bulleted list of their core color's philosophy, and don't worry if they share a few values with other colors.
2. A planeswalker card represents only one facet of a planeswalker, one fraction of their spells, not their whole suite of magic abilities let alone their personality. If you build a character by thinking about how you would depict them, in their entirety, with one card, you unnecessarily limit yourself. Also keep in mind something Brady told us: there is no flavor difference between hybrid and gold.
3. Mages and planeswalkers normally have an affinity for 1-2 colors of magic, or limited schools of magic that they learn earliest and most easily, prefer to use, and keep perfecting over their lives (i.e. telepathy for Jace, pyromancy for Chandra). Since every color has associated values and personality traits, it's not surprising that characters are best at drawing and using the mana that best matches their personality and philosophy.
But planeswalkers can and have picked up other colors of spells as they grow more experienced and visit more planes. Back when they were all immortal, planeswalkers usually ended up quite skilled in all 5 colors, even if most still preferred 1-2 over the others. That isn't likely for most characters now, but there's no reason a neowalker can't dabble in a color outside their usual set of powers if they're exposed to an opportunity and motivation to learn. Nissa dabbled in
magic, for example. She's still a
character at the core and mostly uses
magic. She knows a few
spells, but she's still best at using
. This is the equivalent of putting a splash in a deck. If she started heavily using
magic more than
, I could see it affecting her personality over the long long term, but that's a different scenario.
4. Lastly, when it comes to splashes of off-color magic and bits of off-color philosophy, I see absolutely no reason they have to line up with each other for a character to make intuitive sense. A green character might have white as their secondary color philosophically, but splash black rather than white magic when and if they do learn non-green spells. I don't see any problem there. As a semi-real example, my personality is
first,
second,
third. But if I were a planeswalker my magic of choice would be
plus
with at most a dabble in
.