Oettinger, previously the digital services commissioner, was named in October by commission chief Jean-Claude Juncker to take on the budget and human resources dossier from Bulgaria's Kristalina Georgieva after she left for the World Bank.
But in early November Oettinger was forced to apologise for referring to Chinese people as "slitty eyes" and making disparaging remarks about women, gay marriage and Belgian politicians in a speech.
In an open letter to the European Parliament, which will publicly quiz Oettinger next Monday, NGOs including Oxfam International and Transparency International said that Oettinger was not suitable for the new job.
"Commissioner Oettinger has made racist, sexist and homophobic remarks on several occasions in the past, most recently at a speech he gave in an official capacity in Hamburg on 26 October," it said.
The groups said that at a "crucial moment for the EU" the human resources commissioner should "lead by example" and "speak out against racism, sexism, xenophobia, homophobia and transphobia."
"In our view, Commissioner Oettinger is not the right person for this task."
European Commission spokeswoman Natasha Bertaud said it took note of the letter but had no comment to make on Oettinger's appointment, which became effective on Sunday.
Oettinger's remarks about Chinese people prompted a scathing response from Beijing and red faces at the Commission.
He apologised but said they were meant to give Germany a "wake-up call" over China's increasing power and a debilitating political correctness at home.
The German got into hot water again just days later over accepting a lift in a Kremlin lobbyist's private jet to Budapest without reporting it under disclosure rules. The commission insisted he broke no ethics rules.
For their part, the NGOs said this episode showed "Oettinger is unfit to inspire compliance with existing ethics and transparency rules among Commission staff and his peers."