When we use the expression “a way of life,” we mean that something is or should be an important part of life, that it is an idea or set of conventions, beliefs or values that we should follow.
If we use “be,” - “education IS a way of life,” it is a statement that stands alone and tells us that everyone should seek out education and seek to learn throughout their life, that we all should never stop learning.
If we use “as” - “education AS a way of life,” we are using the expression to describe what it would mean for education. “AS,” is not an affirmation, we are not saying “IS,” so in this case we are likely describing what it means to treat education AS an important part of life (what does life look like if education is an important part of it and we all seek to gain knowledge throughout our entire lives?).
Ex. A person might say something like: “Education as a way of life means seeking education even after our obligatory years of schooling, to continually learn even after we have finished school. It means to adopt a lifestyle where we seek out knowledge, seek to know the world, keep our minds open to new ideas, and so on.”