Traditionally Hindus are the one who believe in Aparusheyatva of Vedas. Swami Prabhavananda says the following in book Spiritual Heritage of India.
The Vedas, on the other hand, are said to be apauruseya, which means
divine in origin. In fact, in the words of Sayanacarya, the learned
commentator on the Vedas, Yo vedebhyaH akhilaM jagat nirmAne — God
created the whole universe out of the knowledge of the Vedas. That is
to say, Vedic knowledge existed even before the creation of mankind.
The authority of the Vedas does not depend upon anything external.
They themselves are authority, being the knowledge of God. And, as we
shall see later, their truth is verifiable by any spiritual
aspirant in transcendental consciousness
Till we reach that state of transcendental consciousness (also can be called as state of Nirvikalpa Samadhi in Yoga terminology) or state of deep tapasya, vedas are to believed by an aspirant and can be verified later through Sadhana. Since Brahman (Ultimate Reality) is beyond senses and mind, we have to first believe visions or first hand experiences of Rishis and then later can verify them in state of transcendental consciousness.
Faith or belief is indeed everywhere. Sri Maheshwaranath Babaji, direct disciple of Mahavatar Babaji explains about Faith to Sri M in book "Jewel in the Lotus - Deeper aspects of Hinduism".
M: With all the knowledge that I have acquired from you, do you think that I will succeed in my path if I have not much faith in you?
I ask this question purely out of academic interest. Please enlighten
me about the proper place of faith in religious pursuits.
Master: Faith is nothing to laugh at. The entire world, including that of science, depends a great deal on faith.
At school, you study all about the universe in your science books.
Since you are not in a position to explore what has been stated – for
instance, that there are nine planets in our solar system that revolve
round the sun – you accept it on faith. Of course, as you grow up, you
might get an opportunity to find out for yourself whether what you
have accepted on faith is true or not. But till then, you pin your
faith on the sincerity of the scientist who stated it and the textbook
that you read.
Would it not be foolish to deny the existence of the nine planets
straightaway because you haven’t seen or you can’t see them? Of
course, the really intelligent student wouldn’t either accept or deny
it straightaway; he would accept it on faith till he finds a means to
enquire into it first hand.
This is the kind of faith that is required of the earnest religious
seeker. He has to merely suspend judgment about the truths the sages
have uttered, after experiencing what is beyond the ordinary man’s
capacity to explore. In the meanwhile, he should try to develop in
himself the faculties that lie outside our sensory organs and
conditioned thought. Once he has reached the same state as a sage who
proclaimed a particular truth, he is at liberty to accept or discard
it. One who denies a statement without enquiry builds a mental
obstruction that blocks all knowledge. How can one seek something
which one has denied off-hand?
You should also note that the word translated into English as ‘faith’
is, in the original Sanskrit, shraddha. Faith is not an accurate
translation of shraddha. Indeed, there are many words in Sanskrit that
do not have a one-to-one equivalence in English. Shraddha, apart from
meaning faith and confidence in oneself, also means one-pointed
attention, the sacred care given to one’s endeavor. When a person has
unquestioned faith in his own capacity for achieving his goal, whether
spiritual or temporal, he is not disturbed by negative thoughts that
weaken the will and discourage the spirit. Not disturbed by any
demoralizing thought, the person who has faith in himself persists in
his efforts till the very end and attains what he sets out to do.
Swami Vivekananda also says the same. The Vedas can be verified in Super-conscious state of human soul.
We have to understand that this consciousness is only the name of one
link in the infinite chain. Being is not identical with consciousness,
but consciousness is only one part of Being. Beyond consciousness is
where the bold search lies. Consciousness is bound by the senses.
Beyond that, beyond the senses, men must go in order to arrive at
truths of the spiritual world, and there are even now persons who
succeed in going beyond the bounds of the senses. These are called
Rishis, because they come face to face with spiritual truths.
The proof, therefore, of the Vedas is just the same as the proof of
this table before me, Pratyaksha, direct perception. This I see with
the senses, and the truths of spirituality we also see in a
superconscious state of the human soul. This Rishi-state is not
limited by time or place, by sex or race. Vâtsyâyana boldly declares
that this Rishihood is the common property of the descendants of the
sage, of the Aryan, of the non-Aryan, of even the Mlechchha.
Now, regarding stories, Mantras human and God names in Vedas, certain philosophers have explained them based on their understanding. For example, Adi Shankara says words like Indra, Varuna has objective counterparts which are eternal and they don't depend on birth and death in his Brahmasutra Bhashya of 1.3.28.
Each word of the Vedas has an objective counterpart, which is not an
individual but a type. The word ‘cow’, for instance, has for its
counterpart the object, which is a type and as such is eternal and
does not depend on the birth or death of individuals belonging to that
type. Similar is the case with words like Indra, Varuna, etc. Words
representing the gods etc. have for their counterpart objects that are
types and not individuals. Again Indra is the name of any one who
would occupy that exalted position, like the word ‘king’ in ordinary
parlance. So there is no contradiction to Vedic words. As a matter of
fact, the world including the gods etc. have originated from Vedic
Jaimini Purva Mimamsa Sutras also explain extensively on same topic. Jaimini says these stories serve as a purpose to glorify the Yajna. So, they are just parts of Vedic injunctions. Jaimini refutes some objections through Arthavada.
अविद्यमानवचनात् ॥ १।२।३४॥ 34.
By reason of the description of
that which does not exist..
The objector says that the mantra describe those things which do not
exist. For example चत्वारि शृङ्गात्रयाअस्य पादा देशीर्षे
सप्तहस्तासाअस्य। (ऋ० म० ४ सू० ५८ ऋचा ३)
He refutes this in Sutra 46 through Arthavada.
अभिधानेऽर्थवादः ॥ १।२।४६॥
अभिधाने in the figurative description.
46. The figurative description is by way of अर्थवाद.
This is in reply to the objection contained in sâtra 34, The description of the
thing not in existence is by way of figurative speech. See for the
explanation of चत्वारि शृगा &c, in the भाष्य ।।
Even six orthodox Schools (Astika Schools) have varied allegiance to Vedas. Swami Viresananda say the following in introduction to Brahma Sutras.
The destructive criticism of everything in the old system by the
Chârvâkas and others set the orthodox section to organize their belief
on a more rationalistic basis and render it immune against all such
criticism. This led to the foundation of the six systems of orthodox
Hindu philosophy -orthodox in the sense that they accepted the
authority of the Vedas in things transcendental - while there were
others who did not accept this authority and therefore were dubbed
heterodox, though otherwise they too were the outcome of Upanishadic
thought. The acceptance of the authority of the Vedas by these
orthodox schools, however, does not mean that they accepted them in
toto . Their allegiance to the Vedas varied widely and often it was
too loose, Of the six orthodox schools, viz. Nyâya, Vaiseshika,
Sânkhya, Yoga, Purva Mimâmsâ and Uttara Mimâmsâ or Vedanta, the last
two are intimately connected with the Vedas, which is one of the
reasons why they are not mentioned in the Jaina and Buddhistic
literature, while the others are mentioned.
Does belief in the Vedas mean (blindly) accepting everything that's stated in them?
So, in short six traditional schools themselves have different beliefs on certain portions of Vedas but they accepted Vedas in things transcendental. So, there can't be one answer for "belief in Vedas or their authority" and it varies with school to school.