The following narration has bothered many for some time due to how many people have spread it without understanding it’s context.
One of the things that most mistakenly do, is to assume that this woman was a non Arab.
Chapter: A black woman (in a dream)Book 91, Hadith 53
The Prophet may Allah’s peace and blessings be upon said, “I saw (in a dream) a jet black woman with unkempt hair going out of Medina and settling at Mahai’a. I interpreted that as a symbol of an epidemic of Medina spreading to it.
باب الْمَرْأَةِ السَّوْدَاءِ
حَدَّثَنَا إِسْمَاعِيلُ بْنُ عَبْدِ اللَّهِ، حَدَّثَنِي أَخِي عَبْدُ الْحَمِيدِ، عَنْ سُلَيْمَانَ بْنِ بِلاَلٍ، عَنْ مُوسَى بْنِ عُقْبَةَ، عَنْ سَالِمِ بْنِ عَبْدِ اللَّهِ، عَنْ أَبِيهِ، أَنَّ النَّبِيَّ صلى الله عليه وسلم قَالَ ‏ “‏ رَأَيْتُ كَأَنَّ امْرَأَةً سَوْدَاءَ ثَائِرَةَ الرَّأْسِ، خَرَجَتْ مِنَ الْمَدِينَةِ،حَتَّى قَامَتْ بِمَهْيَعَةَ ـ وَهْىَ الْجُحْفَةُ ـ فَأَوَّلْتُ أَنَّ وَبَاءَ الْمَدِينَةِ نُقِلَ إِلَيْهَا ‏”‏‏.‏
Ibn Sayadah said in his book Al Muhkum wa Al Muheet Chapter 3 page 209
so they are they Arabs and their colours are Al Udmah (dark brown) and Al Sumurah(brown) and Al Sawaad( jet black)

المحكم والمحيط الأعظم – ابن سيده  ج ٤  ص ٢٠٩

فهم عرب وألوانهم الأدمة والسمرة والسواد

Abu Tayyib Al Laghwhi (350 AH)  said in regards to Fadl Ibn Abbas’s poem,” in his book  kitaab Al Idaad page 162.
” He means that his colour is the colour of the Arabs, and it is jet black”

و قال ابو طيب اللغوي   في كتابه كتاب  الاضداد  ص ١٦٢

يعني ان لونه الون العرب، و هو سواد

And Ibn Yaeesh mentioned in his book Sharh Al Mufassal page 48

The meaning of Al Aswad is because the majority of ( the Arabs ) are brown and jet black in colour.

و ذكر ابن يعيش في كتابه شرح المفصل  ص ٤٨
المراد الاسود لان غالب عليم السمرة والسواد

Secondly, red people  ( very white ) people were rare in that part of the world at that time so one can assume that it was either a jet black Arab woman, a jet black non Arab woman or a jet black Jew woman leaving Madinah as they were the inhabitants of that area at the time.

In Seera A’laam Al Nubalaa, Chapter 2, page 168, Imaam Al Dhahabi , says

Red, in the dialect of the Arabs means a pale white complexion and it was a colour that was rare amongst them.”

سير أعلام النبلاء ج ٢  ص ١٦٨

والحمراء ، في خطاب أهل الحجاز : هي البيضاء بشقرة ، وهذا نادر فيهم

 Thirdly if one wants to make a baseless accusation against the Prophet Mohammed may Allah’s peace and blessings be upon him, then they would have to explain why the following jet black woman was called the ”woman of Paradise”
Bukhari Book 75, Hadith 12 Chapter: The superiority of a person suffering from epilepsy

Narrated ‘Ata bin Abi Rabah:

Ibn `Abbas said to me, “Shall I show you a woman of the people of Paradise?” I said, “Yes.” He said, “This jet black lady came to the Prophet may Allah’s peace and blessings be upon him and said, ‘I get attacks of epilepsy and my body becomes uncovered; please invoke Allah for me.’ The Prophet may Allah’s peace and blessings be upon him said to her, ‘If you wish to be patient you will have enter Paradise; and if you wish, I will supplicate to Allah for him to cure you.’ She said, ‘I will remain patient,’ and added, ‘but I become uncovered, so please supplicate to Allah for me to so that I may not become uncovered.’ So he supplicated to  Allah for her.”

باب فَضْلِ مَنْ يُصْرَعُ مِنَ الرِّيحِ
حَدَّثَنَا مُسَدَّدٌ، حَدَّثَنَا يَحْيَى، عَنْ عِمْرَانَ أَبِي بَكْرٍ، قَالَ حَدَّثَنِي عَطَاءُ بْنُ أَبِي رَبَاحٍ، قَالَ قَالَ لِي ابْنُ عَبَّاسٍ أَلاَ أُرِيكَ امْرَأَةً مِنْ أَهْلِ الْجَنَّةِ قُلْتُ بَلَى‏.‏ قَالَ هَذِهِ الْمَرْأَةُ السَّوْدَاءُ أَتَتِ النَّبِيَّ صلى الله عليه وسلم فَقَالَتْ إِنِّي أُصْرَعُ، وَإِنِّي أَتَكَشَّفُ فَادْعُ اللَّهَ لِي‏.‏ قَالَ ‏ “‏ إِنْ شِئْتِ صَبَرْتِ وَلَكِ الْجَنَّةُ وَإِنْ شِئْتِ دَعَوْتُ اللَّهَ أَنْ يُعَافِيَكِ ‏”‏‏.‏ فَقَالَتْ
أَصْبِرُ‏.‏ فَقَالَتْ إِنِّي أَتَكَشَّفُ فَادْعُ اللَّهَ أَنْ لاَ أَتَكَشَّفَ، فَدَعَا لَهَا‏.‏

Another possibility could be that the woman was from the Children of Israel as they were numerous in Madinah at the time……