According to the explicit teaching of the Qur'an and the practice of the Prophet (peace be upon him) women are active participants with men in all aspects of Islamic life. Allah says, "And [as for] the believers, both men and women they protecting friends and partners: they [all] enjoin the doing of what is right and forbid the doing of what is wrong, and are constant in prayer, and render the purifying dues, and pay heed unto God and His Apostle. It is they upon whom God will bestow His grace: verily, God is almighty, wise!" (Qur'an: 9:71)
It is, therefore, not surprising to see that there was virtually no bar for women on public activity during the Prophet's time. This is a fact well documented in the sources; they were present in the mosques, learning from the Prophet and even asking questions. They were also in the battles, sometimes as warriors, while other times mostly to nurse the wounded as well as to render vital services.
It is high time for Muslims to recognize the fact that the present backwardness of Muslims is in no small measure due to their failure to empower women. It is true that Islam prescribes certain fundamental guidelines for men and women while interacting in public sphere. We should, however, ask why should we place the onus for preserving the morals on women. Why not expect men to shoulder responsibility for the same? In fact, as we could learn from Ibn Abbas, the inspired interpreter of the Qur'an, men should bear a greater responsibility.
Once these limitations are given due consideration and allowance, women should not be barred from publicly participating in any of the activities meant to improve the conditions of the society. How can they be, when Allah places the responsibility for it squarely on the shoulders of both men and women?
Furthermore, women were active in all aspects of public life; they played vital role in changing the status quo; think of Aishah, the beloved wife of the Prophet (peace be upon him). She was a leader, jurist and political activist par excellence; she even commanded the army.
In light of these, I see no reason to find fault with the Muslim girls in participating in such protests, as long as they do so while observing the Islamic rules of modesty and ethics even as boys and men are supposed to. After all, it only shows their concern for improving the lot of the society. Allah says, "Certainly, Allah will not change the condition of people, unless they are willing to change their own conditions" (Qur'an:13:11).