Of course "our own situations with our own internal treatment of indigenous peoples who live in poverty, poor housing and on and on" are a national disgrace. China raises these often with us to try and establish a moral equivalence with their treatment of Tibetans and Uyghurs. In my experience as a diplomat in China with responsibility for the human rights file, this is not annoying to the Government of Canada as so you suggest, but welcomed to open diplomatic engagement on Canada's international obligations to indigenous people. But our First Nations enjoy the protection of the Canadian Charter of Rights and Freedoms. They not subject to arbitrary arrest, and torture to force false confessions simply for standing up for their language, religious and civil rights.
By not speaking out in response to China's oppressive policies we give the Chinese regime tacit consent for their violations of international law as defined by the UN and earlier international bodies such as the Permanent Court of Arbitration in the Hague. Of course if the Chinese regime felt no guilt over their repressive policies against their own people to maintain their power and elite privilege, they would not lash out so emotionally and irrationally against these things being exposed to the light of the day abroad. It has to be abroad as their people live under severe internet censorship and knowledge that speaking truth to power leads to prison camp with no due process of Chinese law. We should give voice to the voiceless.
Standing idly by in the face of injustice is weak and shameful.