The stream of critical CPU vulnerabilities starting with Spectre/Meltdown last year are related to speculative execution, not just Intel. (AMD and ARM CPUs are also vulnerable to Spectre, for example.) Intel CPUs are sometimes vulnerable to additional attacks because they speculate in more scenarios than other designs. But fundamentally, as long as multiple different trust domains are sharing one CPU that speculates at all, or has any microarchitectural state (e.g., caches), there are likely to be some side-channel attacks that are possible.

The important thing to realize is that speculation and caching and such were invented for performance reasons, and without them, modern computers would be 10x-100x slower. There's a fundamental tradeoff where the CPU could wait for all TLB/permissions checks (increased load latency!), deterministically return data with the same latency for all loads (no caching!), never execute past a branch (no branch prediction!), etc., but it historically has done all these things because the realistic possibility of side-channel attacks never occurred to most microarchitects. Everyone considered designs correct because the architectural result obeyed the restrictions (the final architectural state contained no trace of the bad speculation). Spectre/Meltdown, which leak the speculative information via the cache side-channel, completely blindsided the architecture community; it wasn't just one incompetent company.

The safest bet now for the best security is probably to stick to in-order CPUs (e.g., older ARM SoCs) -- then there's still a side-channel via cache interference, but this is less bad than all the intra-core side channels.