Is it permissible for me to participate with the people of innovation in some of their innovations while gradually inviting them to Tawhid?

You can gradually invite them (to the truth), and you may keep silent about some of their transgressions if denouncing them leads to a greater mischief. However, it is not permissible for you to participate with them in performing what you consider an innovation (bid'ah). You must also ascertain by asking scholars before labeling something as an innovation, for there is no denunciation in matters of scholarly disagreement.