What is the ruling on disagreeing with the worshippers by performing an individual takbir after the five daily prayers on the Day of Arafah and the Days of Tashreeq, while trying to initiate the takbir before them, knowing that congregational takbir is an innovation and is widespread in mosques, and that attempting to denounce it may lead to ridicule or anger from the worshippers?

Collective Takbir after prayers during the days of Tashreeq is permissible and not an innovation. There is no need to oppose people regarding it or stir up conflict. The argument that it disturbs those who are catching up on prayers is incorrect, as individual Takbir can also be disturbing. What is required is to lower the voice as much as possible when there are people catching up on prayers. As for Tasbih with prayer beads (subha), it is permissible, but citing their manufacture as a proof for their permissibility is incorrect, as not everything that is manufactured and circulated by people is religiously sanctioned.