I would call C a serious language. Its running your laptop, your phone, your car, the airplane you took on holiday, the fighter planes that protect your airspace, your washing machine, and if you are unfortunate enough to get seriously ill it will probably be running on the medical equipment that keeps you alive.
One of the reasons it is serious is because it is standardized and multiple implementations exist.
So if that's the criteria, then brainfuck is a serious language.
If one wants to use a tool in a life-critical system, a system that might be in use for decades they're going to reach for one of the said "serious languages": C, C++, Ada, etc. That list's very short and it includes neither Brainfuck nor Rust for that matter.
The point is: neither of those two datapoints is a particularly useful metric on how "serious" a programming language is and much less even a useful metric on how well it is suited to any given task. Even how mainstream programming languages are is not a useful signal for that. Javascript is very much mainstream, but I hope no one ever will want to program a cars ECU in a JS dialect. Specialized applications are almost by definition the realm of specialized languages.
Of course most rational engineering organizations wouldn't choose Brainfuck because it's harder to write code that other people can evaluate. But it's not automatically out of the question if you have a good reason for its use.
I did a fair bit of development in C, and developed hard real time systems in VHDL that did involve life & death, but, wouldn't call any language used in the industry generating value as a non serious language...
Off the top of my head I thought C++ and Ada. However, you mention VHDL which I agree with and somebody else pointed out Javascript which is also a good point. The Javascript example (along with C++) make the point that serious computer languages are not necessarily great languages.
I would argue that Rust is not a serious language (at the moment [1]) because its still young, there is no specification and if anything happens to the one implementation it would be a disaster.
Despite C being a null pointer minefield, if someone was to sue a developer the argument could be made that it is an industry standard. In the less likely event that a Rust program hurt somebody what are you going to say?
[1] https://users.rust-lang.org/t/is-there-a-plan-to-get-a-forma...
In practice, though, V8 is the serious impementation. The interesting thing about C and C++ is that I don't know if any given dev is using Clang, GCC, or MSVC until I ask him. I know a JS dev is using V8.