Burqa is not an "Arab tradition" as it is not even an Arab word! It's a Persian word. This is why it is worn in Afghanistan and was once worn in Iran too.
The most conservative dress in the Arab world is the Niqab and a minority of women where that and there is nothing wrong with them wearing that.
Lastly headscarfs are not an Arab tradition as this type of headgear was worn by almost all women in the ME in pre-Islamic times too and in most other places of the world.
Headscarf - Wikipedia, the free encyclopedia
Just because the first use of headscarf is reported to have been used in Southern Iraq by Semites, like most else that was recorded the earliest in history, it does not mean that it was solely limited to the Arab world.
LOL.
Most Shia women in Iraq, Lebanon and Iran wear an Abaya or Hijab.
Since there are 1.5 billion Sunnis, you can find among them the least observing Muslims and the most observing Muslims.
It's complete and utter bullshit that Sunni women have fewer rights than Shia women. Total nonsense.
Sunni women in nearby Kuwait, Syria and Jordan have more freedom than the average Shia Arab woman from Basra, Karbala, Najaf, Amarah, Kut, Nasiriyah, Samawa etc. Southern Iraq is conservative and so is Southern Lebanon and many parts of Iran.
Stop making it sound like you don't wear any headscarfs or live in liberal paradises. I can quickly mention much more "liberal" majority Sunni Muslim nations than the 3 or so Shia majority nations out there. The only exception is Azerbaijan and that's due to Soviet influence. Just like in Central Asia.
Sunni Muslim women can do whatever Shia Muslim women can and probably more than that. They for sure have more important positions out there.