For Huawei they could use national security as an excuse. If Huawei did not have a overwhelming monopoly over network infrastructure then the backlash will not be nearly as severe. For Huawei their overseas arms is only a sales network, local industry wants nothing more than getting rid of them due to competition.Without the US leading anti-BYD policy I don't think the EU will be able to launch a unified approach against it.
Hungary and other smaller euro nations will allow it (if produced from a plant somewhere in Europe / EU), it may find some degree of success in France and other 2/3rd tier car making nations (albeit with substantial tariffs), and may not pick up much in Germany due to the nationalism of consumers favoring German makes.
If Australia is taken as a test case, unless the US starts something then BYD could progress virtually unhindered to take a leading position a few years from now (as Huawei did).
For byd, It's hard to argue for banning BYD from a national security standpoint, as China is already manufacturing a ton of foreign branded cars which it exports all over the world. They're also creating a strong lobby presence by doing a large amount of joint venture and overseas factories, let the locals fight for you instead.