Alleged Contradictions in the Qur'an answer
Does Allah forgive Shirk(non believer-other )?
Verses in question,
4:48 Allah forgiveth not that partners should be set up with Him; but He forgiveth anything else, to whom He pleaseth; to set up partners with Allah is to devise a sin Most heinous indeed.

4:116 Allah forgiveth not (The sin of) joining other gods with Him; but He forgiveth whom He pleaseth other sins than this: one who joins other gods with Allah, Hath strayed far, far away (from the right).

4:153 ...Yet they worshipped the calf even after clear signs had come to them; even so we forgave them; and gave Moses manifest proofs of authority.

25:68,70-71 And those who invoke not any other god along with Allah...and whoever does this shall receive the punishment...Except those who repent and believe (in Islâmic Monotheism), and do righteous deeds, for those, Allâh will change their sins into good deeds, and Allâh is Oft-Forgiving, Most Merciful.
And whosoever repents and does righteous good deeds, then verily, he repents towards Allâh with true repentance.
Shirk is the sin of associating partners with Allah, i.e. attributing divinity or worshipping other than the One Creator.

The explanation of these verses becomes clear if we review the Islamic beliefs one at a time.
1. The first principle is that Allah will forgive ALL sins of anyone who repents sincerely during this life, before their death. This is made clear in the following verse of the Qur'an:
39:53-55 Say: "O my Servants who have transgressed against their souls! Despair not of the Mercy of Allah. for Allah forgives all sins: for He is Oft-Forgiving, Most Merciful. Turn ye to our Lord (in repentance) and bow to His (Will), before the Penalty comes on you: after that ye shall not be helped. And follow the best of (the courses) revealed to you from your Lord, before the Penalty comes on you - of a sudden while ye perceive not!
From the above verse we understand that Allah will forgive all of our sins if we repent before the coming of a "sudden penalty", which refers to death.

2. The second principle here is that after one dies, they are at the mercy of Allah, who may choose to forgive them of their sins or punish them for it, according to what is just. Allah may forgive all of one's sins after they die, except shirk. After a person dies, they will not be forgiven for shirk. The only chance of forgiveness for shirk is if one repents before they die.

3. The above understanding is derived from the Qur'an and the Sunnah, and can be found in many common Tafsir of the Qur'an. For example, Ibn Kathir Ad-Damishqi (d. 1372CE) writes for this verse in his renowned Tafsir Al-Qur'an Al-Azim:
Allah does not forgive shirk, except after repenting from it.(Tafsir Ibn Kathir, Abridged, Darussalam Publishers & Distributors, 2000, vol. 2, p. 481)
And Muhammad Asad comments on the verse:
The continuous stress, in the Qur’an, on God's transcendental oneness and uniqueness aims at freeing man from all sense of dependence on other influences and powers, and thus at elevating him spiritually and bringing about the "purification" alluded to in the next verse. Since this objective is vitiated by the sin of shirk ("the ascribing of divine qualities to aught beside God"), the Qur’an describes it as "unforgivable" so long as it is persisted in, i.e., unless and until the sinner repents (cf. verses 17 and 18 of this surah).(Asad, Message of the Qur'an, The Book Foundation 2003)
And verses 4:17-18 read:
4:17-18 Allah accepts the repentance of those who do evil in ignorance and foolishness and repent soon afterwards; it is they to whom Allah will forgive and Allah is Ever All Knower, All Wise. And of no effect is the repentance of those who continue to do evil deeds until death faces one of them and he says: "Now I repent;" nor of those who die while they are disbelievers. For them We have prepared a painful torment.

Shaykh Abu Ammaar Yasir Qadhi explains the reasoning behind this law:
If a person dies practicing shirk, or not having repented from it, he can never be forgiven for this sin. However, if a person commits shirk before accepting Islam, and dies as a Muslim, then the sin of shirk will be forgiven. This is because a person will be judged by Allah based on his conditions and iman (faith) at the time of death, so if he committed shirk in the past, but eventually accepted Islam, then such a sin would be forgiven. (Qadhi, A Critical Study of Shirk : An Explanation of Muhammad ibn Abd al-Wahhab's Kash al-Shubuhat, Al-Hidaayah Publishing and Distribution 2003, p.22)
Thus, when the verses are interpreted in light of other Qur'anic laws, there is no contradiction.