[RPG] What happens when stepping sideways

I've read most of the sourcebooks and a good bit of the fiction from both the Modern WoD for Werewolf and the Wild Wyld West. I don't recall any specifics on having a red left eye, though sometimes thematically when an eye "glowed red" there was a hint that Wyrm taint was involved. If I recall correctly this was just a descriptive element of the specific tale in order to heighten suspense.

Actual benefit of Kitsune

The paragraph you quoted from W20 Changing Breeds says that:

1. Kitsune can "learn potent Gifts of their own", without a teacher.
2. Kitsune can "learn the Gifts of other Changing Breeds" (any of them), provided that they find a teacher.

The experience cost is specified as "the same as for a non-breed/auspice/tribal Gift", and we don't know if it applies to both points and Kitsune have to pay increased cost if they learn a "potent Gift" on their own.

I do not know if “potent” is just a fluff word here or a game term; as it is not capitalized, I would assume the former.

Let us compare it to the “standard situation of W20” — to the Garou.

Garou, according to the Learning Gifts paragraph on pages 151-152 of W20 Core, always need a mentor to learn a Gift. If it is a Spirit, the process goes fast, if it is another Garou, not so fast, but still possible. Breed, Auspice and Tribe Gifts cost 3*level XP, others cost 5*level XP.

Garou do not get the opportunity to learn the Gifts of other Changing Breeds (other Fera). At least I was not able to find something that allows them to do it, though neither was something directly forbidding it found. The sentence "a werewolf may learn the Gifts of other breeds, auspices or tribes" implies not being able to learn Kitsune Gifts, but rather Gifts of Homid if you are Lupus, for example.

So, in W20 the benefit of Kitsune is not “quantity of Gifts” (the ability to learn more Gifts from their list with the same amount of XP), but rather “quality of Gifts” (the ability to learn more types of Gifts and easy access to Kitsune Gifts). This is further supported by the phrase "Kitsune rely heavily upon their magical strength and versatility."

White Wolf books are flawed

The books printed by White Wolf inherit a lot of text from each other, and when rules (or lore) change from edition to edition, some now unrelated or obsolete text may occasionally stay.

For example, V20 Core, p. 107:

If you don’t have any dots in a Knowledge, you cannot even attempt a roll involving it unless the Storyteller gives explicit permission (such as where common trivia is concerned). If you don’t know Spanish, you can’t try holding a conversation en español on your Wits alone.

But Linguistics is no longer a Knowledge in V20, languages are 1-dot Merits, and you either know it or don't know. This probably still explains how do Knowledge checks work, but the example check is irrelevant. If they changed it to, for example, a Computers check, it would be a lot more relevant, and in addition it would explain what does it mean to have 0 dots in Computers: not being able to use computers at all, or only to hack into the systems?

Or, regarding W20, see the question "How does Calm Heart work?": a Merit from VtM series was directly reprinted without fixing the issue with vampire and werewolf Frenzy functioning differently. You would not be able to use this Merit out of the box, you would have to home-rule some other way to make resisting Frenzy easier or find another book to use.

And the most iconic example being Page XX.

This makes understanding WW books... hard. Sometimes. At least do not expect it to always be easy.

GM fiat is what really limits you ever

You asked about the GM fiat -- here is my answer.

Having to find a teacher to learn a "foreign" Gift effectively means that GM can deprive you of any Gift. He/she may also deprive you of any other option you want to take, just because "Rule 0" gets reprinted in WW books over and over and remains essential, allowing to rule however your ST wants to rule. This is especially important regarding the ability not to look for a teacher when learning a native Kitsune Gift, my inner oWoD player senses tell not to expect every ST to actually allow learning any Native Gift that way.

Whatever is written in the book, all of the GMs that I met had something work very differently compared to RAW, sometimes intentionally (they did not like how it is done by WW), sometimes just because they didn't bother to learn all of the rules. And I also noticed that the more people call some Storyteller I know good, the more are the rules of that Storyteller different from RAW. That is a thing to consider.

Just because it is (un)fortunately not Pathfinder, even if it is possible to do something in oWoD according to RAW, one should be totally ready hear a "no, just no" from the Storyteller.