Is “Son of God” terminology objectionable to all Muslims?
The answer is no. Various Muslim scholars have acknowledged that is not outside the Biblical tradition to give servants of God the title 'Son of God.' Both David and Solomon were called 'Son of God.' Nothing in the Quran rebukes the terminology in this context. The Quranic polemic against the 'Son of God' terminology is against the Trinitarian (Greek/Pagan) use of the terminology. Unfortunately, many Muslims aren't nuanced enough to appreciate that 'Son of God' terminology doesn't necessarily connotate the Greek/pagan idea that God had a literal offspring, that God begets God, or that 'Son of God' is a term indicating being truly God in an ontological sense.
The 'Son of God' terminology should not be objectionable for a Muslim if understood in the Unitarian sense. No Unitarian Christian believes this is a statement affirming that God begat God. It is a statement that Jesus is favored by God. He is the chosen and blessed one who will inherit dominion over all nations. Jesus has this preeminent title, not because he is in his very nature God, but because he has been exalted by God as an honorific title. Thus, the Son of God is a designation of status and not ontology. There should be no objection to the terminology when used in a metaphorical Hebraic sense, as Christian Unitarians do.
The Quranic verses regarding “Son of God” terminology is to rebuke theological claims that Jesus is fully God in an ontological sense.
But the Jews and the Christians say, "We are the Son's of Allah and His beloved." Say, "Then why does He punish you for your sins?" Rather, you are human beings from among those He has created. He forgives whom He wills, and He punishes whom He wills. And to Allah belongs the dominion of the heavens and the earth and whatever is between them, and to Him is the [final] destination.
They say: “The Most Compassionate Lord has taken to Himself a son.” Glory be to Him! Those whom they so designate are only His honoured servants.
Muslim scholars acknowledge the prohibition in the Qur'an is regarding Trinitarian doctrine and theology. These include Shihab al-Din al-Qarafi and Najm ad-Din al-Tufi. These are some classical Sunni scholars who didn't have an issue with the metaphorical usage of the title 'Son of God'. Here is an attestation of their position on this.
This is from page 149 of the by Lejla Demiri on Muslim Exegesis of the Bible in Medieval Cario.
This is from Najm ad-Din al-Tufi's commentary on the Christian scriptures:
Dr. Ali Ataie is a Muslim theologian and professor at Zaytuna college. He doesn't have an issue with Jesus being son of God metaphorically.
The word “son” at times is used, especially in the Bible, to connote “a loved one” and “a favored one.” Instead of comprehending the responsibilities of the position bestowed on the Israelites by God, they wrongly concluded from this bestowal that they were God’s favorites in the absolute sense and arrogantly assumed that they could do whatever they wanted to and God would not hold them accountable for anything they did.
Scholars such as Imam Tufi a Hanbali scholar and student of Ibn Taymiyyah and Shihab al-Din al-Qarafi a Maliki jurist, did not say such things to appease Christians.
The honored slave part is actually simply affirming how Unitarians understand the son of God, its literally makes clear that all these things that are ascribed to these prophets like Jesus or David or any other servant of God called the son of God in the OT or NT, for the most part, is simply an honorary title and not necessarily an attribution of any divine qualities.
Reasonable Muslims will acknowledge that the Quran doesn't deal with semantics, it deals with actual problematic theology, for example when the Quran talks about Mary being deified, this can be argued that this is to address to some forms of Catholicism where Mary is treated like a Goddess despite them saying “we don't worship her.” Reasonable Muslims will understand that the Quran doesn't care about semantics. If the theology is actually problematic, it would call it out, Trinitarianism is problematic. Divine sonship and divine begetting are problematic. Hence, the Quran calls this out, David being begotten by God is not problematic because it's clearly a Hebrew idiomatic phraseology being used in those verses, and it's always been understood this way.