First of all, as I posted in the comment, 純化 is a suru-verb meaning to purify, and 純化にする doesn't make much sense. We never need に there. I believe this sentence should have been:
X + を + [te-form of verb] + た/だ + もの can mean "the product made by ～ing X", "the result from ～ing X", etc. （eg, 刺身【さしみ】とは、生【なま】の魚を切ったものだ。）
Therefore, in this case, 人間の生き方をより純化したもの just means "The human's way of life (itself) which is purified" rather than "An event which purified human's way of life." And the whole sentence means "The death match called 聖杯戦争 is a purified form of human's way of life."
Now, to answer your original question:
Yes, it's also OK to say like this. This sentence is as natural as Sentence A, and means exactly the same thing as A. This is because 純化 happens to be used both transitively and intransitively, which is not the case for many other words which have
～化. (For example, 強化する/美化する is only transitive but 劣化する/進化する is only intransitive. I don't know why.)
In Sentence A, 純化 is used as a transitive verb, whose object is marked with を. The phrase literally means "The thing made by purifying human's way of life." In Sentence B, 純化 is used as an intransitive verb, whose causative form is "[causee]を[verb]させる". The phrase literally means "The thing made by making human's way of life sublime/purify itself."
By the way, the following sentence is also the same as A and B.
In other words, 純化したX, 純化されたX, 純化させたX all roughly refer to the same thing ("purified X"), although there's a small difference in nuance.