I was wondering why a lot of non believers I discuss with about Islam, mostly come up with these two words. As a Muslim myself I do not consider taqqiya to be relevant. Why lie and deceive for the greater good? Or am I wrong about this word?To be honest I don't even fully understand this word. And I also don't understand the word dhimmi exactly. They are protected people under Islamic rule when they pay taxes, if I understand correctly.

Can someone please explain these definitions more and help me in trying to explain it to unbelievers that want to know more about this?

Thank you in advance

Taqiyya

Firstly as a muslim, you are not allowed to lie under any circumstance, Allah says in the Quran:

And cover not Truth with falsehood, nor conceal the Truth when ye know (what it is).  (Qur’an, 2:42)”

“If ye are on a journey, and cannot find a scribe, a pledge with possession (may serve the purpose). And if one of you deposits a thing on trust with another, Let the trustee (Faithfully) discharge His trust, and let him fear his Lord. Conceal not evidence; for whoever conceals it,- His heart is tainted with sin. And God Knoweth all that ye do.  (Qur’an, 2:283)”

“O ye who believe! Stand out firmly For justice, as witnesses To Allah, even as against Yourselves, or your parents, Or your kin, and whether It be (against) rich or poor: For Allah can best protect both. Follow not the lusts (Of your hearts), lest ye Swerve, and if ye Distort (justice) or decline To do justice, verily Allah is well-acquainted With all that ye do.  (Qur’an, 4:135)”

Abdullah bin Mas`ud (May Allah be pleased with him) reported: The Prophet (PBUH) said, “Truth leads to piety and piety leads to Jannah. A man persists in speaking the truth till he is enrolled with Allah as a truthful. Falsehood leads to vice and vice leads to the Fire (Hell), and a person persists on telling lies until he is enrolled as a liar”.’

It was narrated from Abu Hurayrah that the Prophet (peace and blessings of Allah be upon him) said: “The signs of the hypocrite are three: when he speaks, he lies; when he makes a promise, he breaks it; and when he is entrusted with something, he betrays that trust.” (Narrated by al-Bukhari, 33; Muslim, 59)

Hasan bin `Ali (May Allah be pleased with them) said: I remember (these words) from Messenger of Allah (PBUH): “Give up what is doubtful to you for that which is not doubtful; for truth is peace of mind and falsehood is doubt”.  [At-Tirmidhi].

Hakim bin Hizam (May Allah be pleased with him) reported that: Messenger of Allah (PBUH) said: “Both parties in a business transaction have a right to annul it so long as they have not separated; and if they tell the truth and make everything clear to each other (i.e., the seller and the buyer speak the truth, the seller with regard to what is purchased, and the buyer with regard to the money) they will be blessed in their transaction, but if they conceal anything and lie, the blessing on their transaction will be eliminated.’‘
[Al-Bukhari and Muslim].

The term taqiyya came from an incidence in the life of the prophet and demonstrates the mercy of Allah,  A companion  'Ammar b. Yasir,  was been tortured to the point of death to renounce Allah as the one God,  He was tortured so badly that eventually he did succumb,  After this he went to the Prophet (SAW) and told him about this,  Then Allah revealed this verse:

106. Whoso disbelieveth in Allah after his belief except him who is forced thereto and whose heart is still content with
Faith but whoso findeth ease in disbelief: On them is wrath from Allah. Theirs will be an awful doom

This is not a major teaching among most muslims, however If you find yourself in a place where your life is in danger as a muslim, you can be secretive about your religion until you are able to migrate from such a place,  The term taqiyya is mainly used by shia muslims not sunni, 

Most non-muslims twist the concept and make it seem as if you are meant to lie,  Of course not,

Dhimmi

This basically relates to the contract with non- muslims under islamic rule. Non muslims are not compelled by anything in islam except to pay the jizya. Whilst muslims are compelled to pay the Zakat as part of their religious responsibilities. Non -muslims don't pay zakat but pay the Jizya which is normally used to fund the muslim army which provides protection for both muslims and non-muslims in an islamic state and it is the equivalent of jut one dinar. Poor persons, women, children and old folks are exempted. Non-muslims are allowed to carry out their religious obligations in a muslim state without fear of oppression. Islam protects their right.

Non-muslims are supposed to be safe in the hands of muslim in muslim lands.

The Prophets (SAW) said

'the person who would kill a non-muslim under the rein of the muslims, I would come on the day of Judgement and argue against that person'

In another Hadith the prophet said

The person who would harm a Non-muslim under the protection of muslim( a citizen of the muslim state), would not even smell the fragrance of paradise even though the smell can be perceived from far far away,

During the rein of Umar(RA)

There was a Governor of egypt, whose son participated in a race with a coptic christian,  He lost the race and seeing that he was the son of the governor,  He took up a stick and he hit the coptic. The coptic reported this matter to Umar(RA), and Umar was angry. He summoned the son and his father the governor, Then he gave a stick to the coptic and told him to strike the son the way he struck him and then strike the father who had not taught him well.

He famously said ' Who gives you the right to enslave a person who Allah has created free'

So Dhimmi as a contract with non-muslims is to protect their right in a muslim state, 

Unfortunately we see muslims doing things totally against the religion.

I hope this helps

Allah knows best

Walaikum Salaam

UPDATED. ...........