Neither spectre nor meltdown are specific to Intel. They may have been discovered on Intel hardware but the same attacks work against any system with branch prediction or load speculation. The security flaw is inherent to those techniques. We can mitigate them with better address space separation and address layout randomization. That is, we can prevent one process from reading another process's data (which was possible with the original attacks), but we can't guarantee a way to prevent malicious browser tab from reading data from a different tab (for example), even if they are both sandboxed. We also have some pretty cool ways to detect it using on-chip neural networks, which is a very fancy mitigation. Once it's detected, a countermeasure can start screwing with the side channel to prevent leakage at a temporary performance cost.

Also, disabling hyper threading won't cut your performance in half. If the programs that are running can keep the processor backend saturated, it wouldn't make any noticeable difference. Most programs can only maintain about 70-80% saturation, and hyper threading fills in the gaps. However the result is that intensive, inherently parallelizable programs are actually penalized by hyper threading, which is why you occasionally see advice to disable it from people who are trying to squeeze performance out of gaming systems. For someone maintaining a server with critically sensitive data, that was probably good advice. For your home PC, which is low risk... you're probably not worried about exposure in the first place. If you have a Linux computer you can probably even disable the default mitigations if you wanted.