It's a personal belief I think apparent contradictions in Hinduism are trying to tell us something. Does anyone have a good list made by skeptics or unbiased Hindus like those for Bible contradictions?
I am not aware of any good list of contradictions in Hinduism. There is no need for it because unlike the Abrahamic faiths sastra or scripture does not play a stellar role in Dharma. It is experience that is the key to moksha.
They study the Vedas and discuss. But they do not realize the Ultimate Reality just as a spoon does not know the taste of food.
The head carries the flowers, the nose knows the scent. The people study the Vedas. But, very few persons understand the same.
Not knowing the Reality of the self, a fool is infatuated by the sastras. When the goat stands in the shed, the shepherd seeks for it in the well in vain.
The knowledge of the sastras is not competent to destroy the infatuation accruing from worldly affairs.
Having studied the Vedas and realized their essence the wise man should leave all the sastras just as one desiring corn leaves the husk.
Just as one satiated with nectar has no use of food, no one who is in search of Reality has anything to do with the sastras.
One cannot obtain release by reading the Vedas or the sastras. Release comes from experience, not otherwise, O son of Vinata.
[Garuda Purana, Dharma Khanda, Chapter XLIX]
Moreover sastra loses spiritual validity if it does not satisfy the test of reason.
Bhishma said in Mahabharata Shanti Parva Section CXLII:
Even the words heard from an ignorant person, if in themselves they be fraught with sense, come to be regarded as pious and wise. In days of old, Usanas said unto the Daityas this truth, which should remove all doubts, that scriptures are no scriptures if they cannot stand the test of reason.
Mahabharata Shanti Parva Section CXLII
Acharya Shankara, for example, in his Gita Bhasya says:
The appeal to the infallibility of the Vedic injunction is misconceived. The infallibility in question refers only to the unseen forces or apurva, and is admissible only in regards to matters not confined to the sphere of direct perceptions, etc ... Even a hundred statements of sruti to the effect that fire is cold and non-luminous won't prove valid. If it does make such a statement, its import will have to be interpreted differently. Otherwise, validity won't attach to it. Nothing in conflict with the means of valid cognition or with its own statements may be imputed to sruti.
REF: Srimad Bhagavad Gita 18.66 Bhasya of Sri Sankaracarya translation by Dr. A. G. Krishna Warrier, p. 629.
Yoga Vasistha says:
yuktiyuktamupādeyaṃ vacanaṃ bālakādapi | anyattṛṇamiva tyājyamapyuktaṃ padmajanmanā || 3 ||
The remark of a child is to be accepted, if it is in accordance with reason; but the remark of even Brahma Himself, the creator of the world is to be rejected like a piece of straw if it does not accord with reason.
REF: Vasistha's Yoga II.18 translated by Swami Venkatesananda, p 35.
Sri Vachaspati Mishra, another Advaita Vedanta philosopher, says,
Na hy āgamāḥ sahasram api ghaṭam paṭayitum īṣate (Bhāmatī, Introduction)
A thousand scriptures cannot make a jar into a cloth.
REF: Quoted by S. Radhakrishnan in his book, Indian Philosophy, Volume 2.
Moreover even a holy act sanctioned in scripture does not have absolute validity.
When can holy acts be done?
If a holy act is against the interest of other members of the society, it should not be practiced. It is Dharma which is the source of Artha and even of Kama.
Kurma Purana I.2.54
Example of Contradiction:
Enlightened men are those who see the same in a Brahmana with learning and humility, in a cow, in an elephant and even in a dog or in an eater of dog-meat.
The buttocks of a member of an inferior caste should be lopped off in the event of his occupying the seat of a member of a superior caste.
Agni Purana 227.30
While Gita is asking us to treat everyone equally, Agni Purana is contradicting the Gita. Fortunately, the Agni Purana shloka violates the essential teachings of sastra and can safely be ignored.