The lecturer in the video says that one can be a Confucian and a Muslim as long as nothing in it contravenes the Quran and Sunnah. Is this right?

If you consider Confucianism as a monotheistic philosophy which strives to bring order to a chaotic society, then yes, one can be a Confucian and Muslim.

However, this philosophy later on evolved into something called neo-Confucianism, which is actually a syncretism or a combination of different religions. It is an amalgamation of different aspects of Confucianism, Taoism, and Buddhism, which is actually being practised today.  Today, a Confucian follows Confucius, Tao and Buddha at the same time.

Hence, taking this into consideration, one cannot be a Confucian and a Muslim simultaneously. If one is only referring to some of the wise sayings of Confucius, which do not conflict with Islam, then perhaps it may be possible, but definitely not in the state it exists today since it’s a full-fledged religion that incorporates aspects of Taoism and Buddhism as well.