Okay....
"Allah will not call you to account for thoughtlessness (vain) in your oaths, but for the intention in your hearts; and He is Oft-forgiving, Most Forbearing." Surah 2:225
"Any one who, after accepting faith in Allah, utters Unbelief, except under compulsion, his heart remaining firm in Faith - but such as open their breast to Unbelief, on them is Wrath from Allah, and theirs will be a dreadful Penalty." Surah 16: 106
The noted Islamic commentator, Al-Tabary explained Surah 16:106 as a verse that had been revealed to Mohammed after he learned that Ammar Ibn Yasser was forced to deny his faith in Mohammed when kidnapped by the Banu Moghera tribe. Mohammed consoled Ammar by telling him, "If they turned, you turn." (Meaning: if they again capture you, you are allowed to deny me again.)
These and similar passages from the Quran clearly reveal that Muslims' unintentional lies are forgivable and that even their intentional lies can be absolved by performing extra duties. It is also clear that if forced to do so, Muslims can lie while under oath and can even falsely deny faith in Allah, as long as they maintain the profession of faith in their hearts.
In the Hadith, Mohammed, emphasizes the same concept.
From "Ehiaa Oloum al-Din," by the famous Islamic scholar al-Ghazali, Vol. 3: PP.284-287:
One of Mohammed's daughters, Umm Kalthoum, testified that she had never heard the Apostle of Allah condone lying, except in these three situations:
For reconciliation among people.
In war.
Amongst spouses, to keep peace in the family.
One passage from the Hadith quotes Mohammed as saying: "The sons of Adam are accountable for all lies except those uttered to help bring reconciliation between Muslims."
Another says, "Aba Kahl, reconcile among people."(Meaning: even through lying.)
The following quote demonstrates the broadness of situations in which the prophet permitted lying. "The sons of Adam are accountable for all lies with these exceptions: During war because war is deception, to reconcile among two quarreling men, and for a man to appease his wife."
The principle of Al-Takeyya
The Arabic word, "Takeyya", means "to prevent," or guard against. The principle of Al Takeyya conveys the understanding that Muslims are permitted to lie as a preventive measure against anticipated harm to one's self or fellow Muslims. This principle gives Muslims the liberty to lie under circumstances that they perceive as life threatening. They can even deny the faith, if they do not mean it in their hearts. Al-Takeyya is based on the following Quranic verse:
"Let not the believers Take for friends or helpers Unbelievers rather than believers: if any do that, in nothing will there be help from Allah: except by way of precaution (prevention), that ye may Guard yourselves from them (prevent them from harming you.) But Allah cautions you (To remember) Himself; for the final goal is to Allah." Surah 3: 28
According to this verse a Muslim can pretend to befriend infidels (in violation of the teachings of Islam) and display adherence with their unbelief to prevent them from harming him.
Under the concept of Takeyya and short of killing another human being, if under the threat of force, it is legitimate for Muslims to act contrary to their faith. The following actions are acceptable:
-Drink wine, abandon prayers, and skip fasting during Ramadan.
-Renounce belief in Allah.
-Kneel in homage to a deity other than Allah.
-Utter insincere oaths.
So you bring an Islamophobic site as a reference. Since what you quoted must be somewhere in Islamic texts like Quran. You should have quoted them directly....