Absolutely they should!
Contrary to popular belief, God (through His Quran) promotes a democratic system where participation of all citizens is encouraged and facilitated (58:11). Furthermore, He requires election of officials based on qualifications and principles of justice (4:58), and consultation and representation in public affairs (42:38).
58:11 O you who acknowledge, if you are told to make room in the councils, then you shall make room. God will then make room for you. If you are asked to step down, then step down. God will raise those among you who acknowledge, and those who acquire knowledge to higher ranks. God is fully aware of everything you do.
4:58 God orders you to delegate the responsibilities to those who are qualified. If you judge between the people, then you shall judge with justice. It is always the best that God prescribes for you. God is Hearer, Seer.
42:38 Those who have responded to their Lord, and they hold the contact prayer, and their affairs are conducted by mutual consultation among themselves, and from Our provisions to them they give.
In fact, the first democratic system was established when Muhammad was elected as a revolutionary leader by those who accepted his message on their own free will. Even women enjoyed the freedom of voting and pledging for him as recorded in verse 60:12:
60:12 O you prophet, if the acknowledging women come to make allegiance to you that they will not set up anything beside God, nor steal, nor commit adultery, nor kill their born children, nor fabricate any falsehood, nor disobey you in any matter which is righteous, then you shall accept their allegiance, and ask God to forgive them. God is Forgiver, Compassionate.
After Muhammad, the election continued for about thirty years with the elections of Abu Bakr, Omar, Ali, and Usman. Usman's weakness and nepotism lead the Umayyad tribe to take over. Thus, the democratic system, which started with Muhammad, was replaced with monarchy several decades after his departure.
Of course, they can interpret The Quran as a call to action, OR rely on fairy tails and superstition hoping that one day Mr. Mehdi will come and set things straight.
Further reading on how The Quran describes an Islamic state and human rights:
I would vote for that! Wouldn't you?