Recently one of our dear brothers inquired about this, and he ended up writing an article on it. I will send it to you here:

Does the Quran confuse Miriam, sister of Aaron with Maryam, mother of Jesus?
Many anti-Islam scholars claim that the Quran made an error when ‘revealing’ the following verses:
فَأَتَتْ بِهِ قَوْمَهَا تَحْمِلُهُ ۖ قَالُوا يَا مَرْيَمُ لَقَدْ جِئْتِ شَيْئًا فَرِيًّا
“And she came to her people with him, carrying him (with her). They said: O Marium! surely you have done a strange thing.” (19:27)
يَا أُخْتَ هَارُونَ مَا كَانَ أَبُوكِ امْرَأَ سَوْءٍ وَمَا كَانَتْ أُمُّكِ بَغِيًّا
“O sister of Haroun! your father was not a bad man, nor, was your mother an unchaste woman.” (19:28)
Their argument is that Muhammad (saw) believed that Miriam, sister of Aaron and Mary, mother of Jesus was one and the same person.
Answer:
The Quran does not confuse both women at all, as the term ‘sister’ used is not a literal biological relationship.
In order to understand this further, we need to be aware of the following:
1. We need to look at the term ‘Aronite/Aronide’, which literally means ‘A descendant or follower of Aaron; a member of the Jewish priesthood”.
2. Idioms used in Semantic languages

Aaronites/Aronides and their role:
It is a known fact that Aaron and his descendants were exclusively chosen as caretakers and high priests of the Holy Temple in Jerusalem. Anyone serving at the temple was given the honorary title of ‘Aaronide’.

The Bible uses the term ‘sons of Aaron’ for his descendants several times (Exodus. 27:21, 28:43, 30:8) (Leviticus 6:9) and many other places.

Since Mary, mother of Jesus was of priestly descent and had lived in the temple from early childhood, the term ‘sister of Aaron’ has been used as an honorific term title, which was common in Hebrew.
Scholars such as Angelika Neuwirth and Nicolai Sinai both attest to the above.

The term ‘sister of Aaron’ was used by the Israelites to make her feel ashamed for what they thought was ‘fornication’ by reminding her that she belonged to a priestly family.
The above statement is supported by a narration in Muslim:
Mughira b. Shu‘ba reported: When I came to Najran, they (the Christians of Najran) asked me: You read "O sister of Harun" in the Qur'an, whereas Moses was born much before Jesus. When I came back to Allah's Messenger (may peace be upon him) I asked him about that, whereupon he said: "The (people of the old age) used to give names (to their persons) after the names of Apostles and pious persons who had gone before them."

Idioms used in Semantic languages
Those who are unaware of the Arabic language’s use of Idioms/epithets are the ones putting forward the claim above. Someone learning Arabic finds the idioms/epithets the hardest, because the words by word translation does not mean what’s intended and the learner finds it extremely confusing. We see the same with the Quran and the term يَا أُخْتَ هَارُونَ (sister of Aaron).
It has to be noted that the term يَا أُخْتَ هَارُونَ as per the Quran was used by the Israelites. Allah calls Mary, the mother of Jesus, مَرْيَمَ ابْنَتَ عِمْرَانَ (Mary daughter of Imran).
The words "sister", "brother", "son", "daughter" and “father” in Arabic usage can have a wide connotation. As an example of “father”, the Quran states: وَإِذْ قَالَ إِبْرَاهِيمُ لِأَبِيهِ آزَرَ (Lo! Abraham said to his father Azar 6:74). In the above verse, the word ‘ Ab ‘ has been used for Azar. However, ‘Ab’ has different meanings and does not necessarily mean ‘Walid’ (biological father).
The word ‘ Ab ‘ in Arabic language can mean father as well as ancestor or even uncle as Ismail the uncle of Yaqoub has been addressed as ‘ Ab ‘ in the following Qur’anic verse:
قَالُوا نَعْبُدُ إِلَٰهَكَ وَإِلَٰهَ آبَائِكَ إِبْرَاهِيمَ وَإِسْمَاعِيلَ وَإِسْحَاقَ
“They said, ‘We will worship your God and the God of your fathers, Abraham, Ishmael, and Isaac…” (2:133)
Since Ismael was not the father of Jaqoub, and yet Quran uses the word ‘Ab’ for him as uncle, then the usage of this word for other than biological father is established.
The wide usage of the Hebrew word ’achôwth’, the equivalent of Arabic ukhtun, meaning "sister", is also attested in the Hebrew Bible:

The online Blue Letter Bible, under ’achôwth’, lists the following usages in the Bible:
• sister (same parents)
• half-sister (same father)
• relative
• (metaphor) of Israel's and Judah's relationship
• Beloved
• Bride (fig.) of intimate connection

Now let’s take a look at Quranic verses where “sister’ has been used as same idiomatic expression:
قَالَ ادْخُلُوا فِي أُمَمٍ قَدْ خَلَتْ مِنْ قَبْلِكُمْ مِنَ الْجِنِّ وَالْإِنْسِ فِي النَّارِ ۖ كُلَّمَا دَخَلَتْ أُمَّةٌ لَعَنَتْ أُخْتَهَا ۖ حَتَّىٰ إِذَا ادَّارَكُوا فِيهَا جَمِيعًا
He will say, ‘Enter the Fire, along with the nations of jinn and humans who passed before you!’ Every time that a nation enters [hell], it will curse its sister [nation] (7:38)

وَمَا نُرِيهِمْ مِنْ آيَةٍ إِلَّا هِيَ أَكْبَرُ مِنْ أُخْتِهَا ۖ وَأَخَذْنَاهُمْ بِالْعَذَابِ لَعَلَّهُمْ يَرْجِعُونَ
We did not show them a sign but it was greater than its sister, and We visited on them punishment so that they might return to faith. (43:48)

Conclusion
Those who take “sister of Aaron” literally have clearly a lack of Arabic language skills. The Arabic language and the Quran has used idioms several times and the fact that the Hebrew Bible does the same, attest that “sister of Aaron” is not to be taken literally.