Does Not Wearing Hijab Render One out of the Fold of Islam?

Assalamoalikum scholars, I wanted to inquire about the meaning of the following verse of the Holy Quran:allah Almighty says: "O Prophet! Tell thy wives and thy daughters and the women of the believers to draw their cloaks close round them (when they go abroad). That will be better, so that they may be recognized and not annoyed. Allah is ever Forgiving, Merciful." (Al-Ahzab: 59) I want to know that here in the verse it says ?so that they may not be recognized? here does it refer to the fact that hijab will help distinguish between muslim and non muslim females in the same way that maybe a beard and a muslim cap distinguishes between a muslim and non muslim male?I mean that these things also act as muslim labels especially in an environment where there are muslim and non muslim people together. So what I want to know is that if for example in a mixed environment(muslims non-muslims together) if a muslim male or female doesn?t have an Islamic label on him or her like a beard or hijab or anything which would show his or her Islamic identity and there is a risk that they maybe considered a mushrik because obviously no other person would have a good enough reason to assume that they are muslims on sight especially in a mixed environment where muslims and non muslims are dressed alike(I don?t mean to say that muslims have on certain religious symbols of other religions I just mean that they are dressed such that there is no differentiating factor that whose a muslim and whose a non muslim)so will that put that person out of the fold of islam? I also want to know if this hadith is authentic. I don?t remember the actual quotation but the central idea was that our prophet Mohammad(peace be upon him) said that there will come a time that salat would remain as the only differentiating factor between a muslim and a mushrik.Please explain if this hadith is authentic then what is the reconciliation between the above ayat, what I have asked you and this hadith? May Allah bless you all.