I have simplified it.
1. The Malays don scarfs and songkok and had a distinct dress code that was nowhere near that of the Arabs until the 70s.
2. I have no doubt there are variations within the dress code within the Middle East. I am told the Indians can tell the region in India where a woman comes from by the way the woman dons the sari. But you know that it cannot be similar to anything else worn around the World.
3. I seriously doubt the tudung and Hijab has nothing to do with politics and purely one of religious conviction and a "deep personal choice" for the majority of Muslims here. You see the same trend all over the World from the UK, US, Europe etc.
4. Compared to the past, the Muslims are unlikely to accept invitations to the homes of non-muslims for a meal and vice versa. Again nothing to with religion but community pressure to toe the line.
5. Sadly in recent years, some Muslims have politely turned down wedding invitations from colleagues and friends even when the usual practice of having muslim tables are made available. I am also aware that non-muslims colleagues have joined Muslim tables to make the numbers and not isolate their muslims colleagues and friends who have graciously accepted the invitations.
6. I am absolutely certain that vast majority of Muslims are decent and kind people but community pressure is quite intense.
7. As to weather, climate and geography, it makes absolute sense that Arabs chose their particular dress code. Our part of the world does not have intense heat, scorching sun rays nor sand storms.
Ours is a secular society. We deported the Niven Road Sikh priest for asking Singapore Sikhs to don black turban at the height of the Kalistan affair and the same concerns applies here. By the way the Songkok was part of the Singapore Civil Service dress code for males in certain vocations but fell out of flavour and I am sure there would be no objections if it makes a return.
By your logic then Islam is just the religion of the Arabs so should similarly not have encroached on Hindu Nusantara? The tudung/hijab is a piece of cloth that is meant to encourage modesty (not force it). Certain Meditarranean and Central Asians communities also have a similar concept of modesty for women (eg. Greece and Cyprus so it is not particular only to Muslims). I suggest to have a look at photos of the Gulf Arabs at the turn of the century in particular the women - they looked nothing like what they do now in terms of dress - it was not a sea of white and black in the Gulf states (again the label Arab is generic and inappropriate to use in such a wide-brushed manner so let's be specific).
Also note that the Arabs of Yemen do not dress like the rest of the Gulf states except for Oman (which is not a Sunni state). I agree that the enforcement of the notion of increased religiosity to show adherence to faith is the issue here - even Faisal's declaration that as a Muslim father it is a dear matter is hogwash as it stems for an interpretation of responsibility that is misplaced when applied to minors.
Anyway your point about the weather here is also silly - the weather in the Gulf is much more brutal than Singapore. In actuality the Gulf Arabs don white and black as it distinguishes them as locals/natives from the foreigners and for cultural reasons - the sheyla is also a cultural manifestation which varies in presentation depending on tribes and where you may be (look at the girls in Bahrain who are very influenced by the lowering the sheyla half-way down their heads in emulation of the styles of Iranian girls (who are not Arabs)). Again it is not done for strictly religious adherence but for their tribal/cultural requirements. This is the part that the locals in Singapore/Malaysia just don't understand and grasp.
Unfortunately no matter how much one tries to inform the local Muslims here they just don't see it because they have never been there or lived there for prolonged periods of time. They live in la-la-land thinking that just because they are Muslims they will be embraced and celebrated when they are in those societies - nothing is further from the truth. Also if you are around Orchard Road you will see Gulf Arabs dressed quite liberally in Westernised clothes with a colourful tudong - it amuses them to no end to see local Malays dressing in black abayas and tudungs and men in white thobes when it has nothing to do with their inherent culture.
I don't disagree with Alfian completely as he is not being dishonest that there is pressure in the local Malay community for girls to don the hijab and some do in order to liberate themselves somewhat - again it is a generalisation to think each one is doing it for that same reason. But it is a perspective of some. The advent of the internet has also changed everything. No longer do you need to go to the mosque to learn about your faith - just look at your phone and videos aplenty but you can also be easily misinformed because laziness typically means you accept at face value without checking the source of information. One seller of hijabs said there are multitudes of women who regularly watch Youtube videos to try and out-do one another in terms of how they tie their hijabs and it is a fashion thing. Again, some not all.
The rise of the hijab has also coincided with the militancy of those requiring halal only cafes and restaurants. Look at the queues outside the new burger bar opened by Fat Boys in Arab Street - a smart move for him to team up with Sheikh Haykel and going Halal by not diluting his original brand equity.
You will note especially if you are in the vicinity of Little India that the majority of women wearing black abayas are the South Indians Muslims - a rather quiet community that have been wearing the black abaya for years without making a song and dance about it as it is their community identity.