Praise be to Allah.
Reciting the Talbiyah in unison was not related from the Prophet (blessings and peace of Allah be upon him) or from his Companions. Hence a number of scholars stated that this is an innovation (bid‘ah).
It says in Fataawa al-Lajnah ad-Daa’imah (11/358): What is the ruling on pilgrims reciting the Talbiyah together, whereby one person says it and the others follow?
Answer: It is not permissible to do that because it was not narrated from the Prophet (blessings and peace of Allah be upon him) or from the Rightly Guided Caliphs who succeeded him (may Allah be pleased with them). Rather it is an innovation. End quote.
This applies to those who deliberately recite the Talbiyah in unison. As for the one who is reciting the Talbiyah with other people nearby, and their voices coincide unintentionally, there is no blame on him.
What usually happens when people are together, reciting the Tabliyah out loud, is that their voices will coincide sometimes. If the people around you are reciting the Talbiyah in unison, you should not keep quiet; rather you should recite the Talbiyah out loud too.
If you are afraid that this may result in negative consequences, if the people around you notice that you are reciting the Talbiyah on your own, then recite in a quiet voice, But remaining silent is not appropriate, because the Talbiyah is a righteous deed and a beneficial act of worship.
An-Nasaa’i (2753), at-Tirmidhi (829), Abu Dawood (1814) and Ibn Maajah (2923) narrated from as-Saa’ib ibn Khallaad that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Jibreel came to me and said: ‘O Muhammad! Tell your companions to raise their voices when reciting the Talbiyah.’” Classed as saheeh by al-Albaani in Saheeh an-Nasaa’i.
A version narrated by Ibn Maajah says: “Let them raise their voices when reciting the Talbiyah, for it is one of the symbols of Hajj.”
At-Tirmidhi (827) and Ibn Maajah (2896) narrated from Abu Bakr as-Siddeeq that the Prophet (blessings and peace of Allah be upon him) was asked: Which (actions of) Hajj are best? He said: “Raising the voice in Talbiyah and slaughtering the sacrificial animal.”
Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
And Allah knows best.