Not as likely as you think, the UK is already saying it won't comply with the US directive once certain safeguards are made, and the rest of us outside the US mostly figure that most networking equipment has backdoors in it for the NSA anyway so it's little difference to us if there's a backdoor to another country.
The US has been trying to pressure Europe to dump them for a while now (months), and a lot of European countries have just openly refused. I sincerely don't think any other country is going to jump on board.
The superpowers have more risk when it comes to infrastructure and privacy (direct warfare doesn't work reliably enough and they are in the dominant positions), and they also have the luxury of being able to homebake some stuff (potentially). Everyone else has to depend on the global market, and don't have to worry as much about that.
Like if China wanted to take, say australia, they'd just do it. They face backlash, and retaliation from the international community sure, but they wouldn't need hacking, infrastructure attacks, intel etc. They could just brute force it. And so it's not as big a concern for anybody else.
Infrastructure is a superpowers vulnerability point (which is also why this is a cold tech war, not a trade war; the pretext is trade, but the reality is China and the US govts are afraid of each other militarily, as Russia and the US were during their cold war).
The US is also limited in it's ability to cut off ties. So is China. They can't make everything. They can ban Huawei or apple, but if they start banning anybody that trades with them, they'll quickly find their economy in a mess.
I'm sure it'll effect everyone else, but unless some crazy trade deal is offered, with large benefits, I don't see anyone else joining in. Especially because Huawei is a leader in 5G (and dominant in certain markets phone wise)
Facebook
Twitter
Instagram