It's not a "border" in the sense that it's a national border, so the "Chinese" no more "cross" that border than the "Canadians" do when they enter Quebec. It's all China.
There is no dispute as to the sovereignty of Hong Kong, like there is with, say, Taiwan. Hong Kong is part of the PRC. So the most we COULD do is suspend some levels of diplomatic contacts, like we did after Tianamen Square. I'm not even sure we'll do that.
Now, what do YOU think?
It's a national border for the purposes of visa issuance to foreigners and "visa run" updates by foreigners.
The foreigner needs a stamp in your passport from each government -- Beijing and Hong Kong. Without either stamp you can't transit to the other. It's not like Canada at all, not in the least bit, and not ever. For foreigners, and for purposes of visa and passport, the border at the Mainland and Hong Kong is a national border
This is due to the local autonomy Hong Kong has. Hong Kong is a Special Administrative Region of the People's Republic of China. HKG is not a province of the PRC. I've been entering the Mainland via Hong Kong SAR for 10 years. And exiting the mainland to Hong Kong SAR for 10 years. I need a stamp of approval from each government to transit the border that separates 'em. Every foreigner does.
For Chinese nationals they need a border pass to transit from one place to the other, ie, Mainland to Hong Kong and vice versa. For Chinese nationals, you can't transit the border checkpoints to either destination without the border pass. Beijing issues a Hong Kong border pass to Chinese nationals on the mainland. In Hong Kong the local government issues a border pass for residents of Hong Kong to transit to the Mainland. In either instance an application for a border pass must be approved by the jurisdiction in which you reside, ie, the PRC or the HK SAR.
In the HK SAR the local government controls border crossings by every person, foreigner or Chinese national, into it and out of it. Beijing does the same on the mainland in respect of Hong Kong residents and foreigners alike.
For the Chinese population this is apart from the Hukou system. Under the Chinese Hukou system each Chinese needs a pass issued by the government to relocate outside of his birthplace city, town, village, province. A Chinese without the Hukou system pass and who considers his village of birth to be a death sentence, can't escape legally unless he can secure a Hukou certificate from the Party-Government. So if you go outside of your home village or jurisdiction without the Hukou cert/card you become an illegal migrant. Which means You can't get a decent job or any job, rent or buy housing, can't enroll your kid in school, get hospital or medical treatment and so on and so on.
There are no such lunatic arrangements in Canada of the Hukou internal domestic passport as there are in the CCP-PRC. That is, Canada is civilized up to modern standards; China is not. Presently 250 million Chinese are illegal domestic migrants without the internal domestic passport. They cluster outside the cities and live on less than $2 a day. Mao created Hukou and each year during the period of China's expansion the Party vows faithlessly and idly to reform it.