"I don't have any opinions."
Okay, but taken alone without other context this looks like 'I don't have any objections.' I more neutral way to say this would be ‘我没有什么想法／看法。’
This Chinese sentence should not have been translated literally, like what Duo did.
The actual meaning when people say it, is "I have no objection."
Although literally the Chinese sentence means I don't have any opinion, and Chinese do not have a culture of individualism, it is still a shame to say I do not have any opinion, as if I am dummy. At most people would say I do not have other opinions / 我沒有其他意見 or I do not have anything/any other opinions to supplement 我沒有(東西/意見 要)補充. 10 out of 10 times they mean I have no objection.