SMT (a.k.a. hyperthreading) is kind of a security minefield, but so is out of order execution and crufty instruction sets like x86_64. But vulnerabilities of this sort tend to be hard to exploit in the wild. Not saying you shouldn't be concerned about them, but how concerned you are should depend on your threat model. If I were really paranoid and could pick I'd choose something like a low-power simple ARM or RISC-V core to do critical computation. Alternatively you could run your secure compute on any system as long as nobody is allowed to run any other code on that system or have physical access to it.
BTW I am deeply surprised that there has never been a cloud hypervisor doomsday vulnerability that has brought down AWS or some other huge provider. Back when virtualization in the cloud got big I would have bet serious money that this would have happened by now.