They do not have any rights over you, other than the general rights of brotherhood between believers.
Islam is a divine religion that Almighty Allah revealed to guard the welfare of people. Almighty Allah knows the reality of things and what benefits His slaves, so He set laws accordingly for them to observe. Since Islam is the seal of religions, these laws are for until the end of this world. Because of corruption, badness and evilness in certain things or acts, He commanded us to refrain from them and made them prohibited. Similarly, because of benefits and goodness in certain other things, He ordered us to perform them and made them obligatory on us. Some of these laws are general and apply to all people, all the time, and anywhere.The ability of the human being is limited, so is unable to find out and understand the reasons behind the Sharia of Almighty Allah. Sometimes Allah Almighty has taught us through the Holy Prophet and the Imams (peace be upon them), the wisdom behind certain few rulings. We must obey His laws by refraining from the prohibited acts and undertaking the obligatory acts, even if we do not know the reason behind each and every one of them.The najasah of the dog is one of the rulings about which we do not know the wisdom behind.
Whoever submits to the two testimonies – that there is no god but Allah and Mohammad (peace be upon him and his holy progeny) is His messenger – then he is a Muslim and not considered as a non-believer, even if he believes in false beliefs or certain misguidance.
The imamate of the Ahlulbait (peace be upon them) can be proven from the holy Quran by a number of ways. Amongst them: - "Your guardian can be only Allah, and His messenger and those who believe, who establish worship and pay the poor due while bowing down (in prayer)." (Quran 5:55) This verse was revealed at the incident where Imam Ali (peace be upon him) gave his ring as charity while he was bowing in prayer. The verse joined his guardianship to the guardianship of the messenger of Allah, which is the leadership of the Muslim nation, i.e. the Imamate. - "Nor does he speak of (his own) desire" (Quran 53:3). The verse indicates that what the Prophet says is from Almighty Allah. The orders of the Prophet were to follow his household when he said in this commonly known narration: “I leave among you the two weighty things: the book of Allah and my progeny; as long as you are attached to them both, you will never be misguided." The Prophet also ordered us to follow Imam Ali in the famous narration of Ghadeer: "Whosoever’s master I am, Ali is his master." In another narration, the Prophet said: "Ali is your master after my demise," and many more narrations.