Here's my take, sharing what was taught to me
Thus Have I Heard...
Are there certain sutras which are of more relevance to some Mahayana schools than others?
The answer may be 2 fold:
Yes, in terms of specific usage in teaching, reference and practice.
Pure Land Tradition: The Threefold Pure Land Sutras
The Nichiren Tradition: The Wonderful Dharma of the Lotus Sutra
The Ch'an/Zen Tradition: The Lankavatara and Wisdom Collection of Sutras
The Esoteric Tradition: The Mahavairocana and Vajrasekhara Sutras
No, in terms of general usage. All Mahayana Sutras (whichever recognised Mahayana Canon they are derived from) are accepted by most as valid sources of the Buddha's Word. It may be expressed in this way: (using the Pure Land Tradition):
The Threefold Pure Land Sutras are the core/primary source when it comes to specific, teaching, reference and practice but...we also have:
Stage 1: Other 'anchilary' Sutras supporting references like Chapter 40 of the Avatamsaka Sutra, the Chapters on Avalokitesvara and Mahastamaprapta, the Pratyutpanna Samadhi Sutra and other Esoteric Sutras which are used as favourable references to the Pure Land teaching, reference and practice.
Stage 2: Sutra studies of other scriptures as part of learning and familiarize oneself in the Sutra Pitaka to understand what other parts of the Buddha Dharma that we need to know and learn. After all, to embrace the Sutra Pitaka is part of the Bodhisattva's aspiration.
Are there some schools to which some Mahayana sutras are irrelevant, or possibly contradictory to the teachings of that school?
On the surface and for the uninitiated, it may seem so.
For example: The Threefold Pure Land Sutras and compared to the Lankavatara/Diamond Cutter Sutras.
To those in the Ch'an/Zen Traditions, the 'reality' of the Pure Land is ultimately an empty phenomenon.
But to those in the Pure Land Tradition, it is viewed from both of the phenomenon and neumenon levels.
One is approaching the Dharma Door of Emptiness, another is viewing via the Door of Existence.
Another example is The 'True Self', 'Permanency', 'Buddha Nature' and so forth as espoused in the Mahaparinirvana Sutra may seem 'anathema' to those who regard Lankavatara/Diamond Cutter Sutras as authoritative.
Before one jumps the gun, one must know what was the intended audience, time, place, capacity of living beings in that Dharma Assembly when the Buddha delivered His Sermon. And Sutras should be read systematically and together to obtain maximum benefit. (another topic by itself)
Many read the Sutra Pitaka in a fragmented manner and to be fair, not to be blamed too, due to limited resources and constraints. So one would end up with fragmented ideas and form opinions that may seem to express contradiction and irrelevance for some. One example is the case of early Chinese Buddhists, where they held that one who is an icchantika (the most based or hopeless of beings who are incapable of spiritual insight) were thought as never to attain Enlightenment and one Chinese Lotus Sutra commentator went against this idea. He was suppressed and persecuted. But when the Mahaparinirvana Sutra came to Chinese shores, it held the same as the commentator, that all sentient beings have the Buddha Nature and are therefore capable of Awakening and Enlightenment. The reviled 'heretic' was elevated to be a 'saint'.
1. We cannot reject any part of the Sutra Pitaka, being the Buddha's Teaching Body itself which contains the wisdom and liberation needed for our practice and liberation.
"Shariputra, the Thus Come Ones have only a single Buddha vehicle which they employ in order to preach the Law to living beings. They do not have any other vehicle a second one or a third one"
Shariputra, the Law preached by all the Buddhas of the Ten Directions is the same as this."
2. The concept of 84,000 Dharma Doors will come into play here where each of it was taught by Him to reach to a specific class of existence and also generally.
3. What is 'ultimate' to one Tradition may be 'anchilary' to another, it goes back to our understanding that limitless beings are out there, so we also aspire towards learning the limitless Dharma doors to reach out. Small minded sectarianism is not only limiting, it is also a hindrance.
4. To even say or proclaim that any part of the Sutra Pitaka is 'irrelevant' or 'contradictory' reveals one's own poor understanding/misunderstanding of the Buddha's scheme of compassion and liberation.
"Good men, the Scriptures expounded by the Thus Come One are all for the purpose of saving and emancipating living beings. Sometimes I speak of myself, sometimes of others: sometimes I present myself, sometimes others; sometimes I show my own actions, sometimes those of others. All that I preach is true and not false."
"Because living beings have different natures, different desires, different actions, and different ways of thinking and making distinctions, and because I want to enable them to put down good roots, I employ a variety of causes and conditions, similes, parables, and phrases and preach different doctrines. This, the Buddha's work, I have never for a moment neglected."
5. And with regards to sectarianism born either from unintended or wilful ignorance of other parts of the Sutra Pitaka or just plain religious overzealous bigotry:
“Further, Manjushri, in the future Ending Age, when the Dharma is about to become extinct, the Bodhisattva Mahasattva who receives, upholds, reads, or recites this Sutra should harbor no thoughts of envy, flattery, or deceit. He should also not ridicule or malign those who study the Buddha Way, nor should he seek their strengths or weaknesses.
If there are Bhikshus, Bhikshunis, Upasakas, Upasikas, those who seek to be Hearers, Pratyekabuddhas, or those who seek the Bodhisattva Way, he should not torment them or cause them to have doubts by saying to them, “You are all very far from the Path, and you will never obtain the wisdom of all modes. Why not? Because you are careless and lax in the Way.”
Further, he should not frivolously discuss the Dharma for the sake of argument.”
And a related admonition from the Sixth Patriarch of Ch'an:
http://www.dharmaweb.org/index.php/Sutr ... structions
"A bigoted believer in Nihilism blasphemes against the Sutras on the ground that literature (i.e., the Buddhist Scriptures) is unnecessary (for the study of Buddhism). If that were so, then neither would it be right for us
to speak, since speech forms the substance of literature. He would also argue that in the direct method (literally, the straight Path) literature is discarded. But does he appreciate that the two words 'is discarded' are also literature? Upon hearing others speak of Sutras, such a man would criticize the speakers as 'addicted to scriptural authority'.It is bad enough for him to confine this mistaken notion to himself, but in addition, he blasphemes against the Buddhist scriptures. You men should know that it is a serious offence to speak ill of the Sutras, for the consequence is grave indeed!
This is what Chinese Mahayana Buddhists and also some from the Japanese Zen Tradition recite/sing before reciting any Sutra (from the Tang Dynasty's only female Emperor, a great patroness of Buddhism, Wu Ze Tian):Sutra Preface Verse/(開經偈) 'Kai Jing Ji'/'Kaikyouge'
"The Unsurpassed, Profound and Wonderful Dharma,
Difficult to encounter in hundreds of millions of Aeons,
Now do I see and hear, receive and uphold It,
Vowing to fathom the Thus Come One’s True Intent"
Namo Amitabha Buddha!