The definition of being white, like all definitions, can indeed vary based on time and place, yes. Whether someone is white "enough" to be included in the category of "white people" is not an objective fact and will change from culture to culture, from time to time, and even from one individual perspective to the next.

Racial categories in Europe were more complex than they generally are today, especially in America. It's difficult to maintain distinctions in race between different European nationalities when everyone's immigrating to the same place and having kids together, so over time these subtle distinctions have dropped off somewhat in favor of the simpler categories of "white" and "non-white." But some of these distinctions still remain, for instance, many people who identify as "white nationalists" or even "white supremacists" also hate Jews, including Jewish people with white skin. Hitler's infamous 14 words declare that a future must be secured "for our white children," yet clearly he did not consider white-skinned Jewish people to be included in that definition.

As absurd as it may be to say that someone can have white skin but not be considered white, it can happen. The reason it doesn't make sense is because race is, to a large degree, something that is socially constructed and nonsensical.