rust currently has only one backend, which is LLVM, but their is a working project to build an alternative one for the Cretonne compiler[1] for the «debug» builds, and there might also be a GCC backend for rustc one day if people are interested enough to build it. I'm not aware of any fundamental difficulties that would prevent it.
[1]: https://internals.rust-lang.org/t/possible-alternative-compi...
The language with the most sensible implementations seems to be javascript, I guess.
That said, Microsoft has very deep pockets, shows every indication of continuing to promote and use .NET extensively, and has also built up a lot of commercial buy-in over the 15 years or so that .NET has existed, which could carry it forward a while or fuel alternate implementations if something catastrophic happened.
PyPy is a serious implementation of Python. There are others and have been others over the years. While the corporate buy-in isn't the same as .NET or Java, there is a large amount of open source funding and buy-in from very diverse sources. Python is older than .NET as well.
Maybe the risk of using Rust is acceptable even if a bit larger, or the added risk is offset by Rust's good qualities - nonetheless, it's a very new language with no Microsoft-scale company behind it. Not precisely comparable.
It doesn't matter if Rust is perceived as having less ecosystem risk than Python or .NET, if in (say) 10 years it doesn't make significant headway against C, which is what it actually has to compete with. Here we could consider the examples of Pascal and Lisp - they competed with C, were arguably much better languages, and they lost anyway.
It's something worth considering if your dreams are founded on Rust.
Or avoiding Flash because only Adobe supports it, or SilverLight/VB because only MS supports it, or Objective C because only Apple supports it.
That's not necessarily a bad thing since the compilers are all open source and you can port them to whatever platform you want anyway. C managed to spawn a lot of adequate compilers, but the language itself has seen very few changes since it was standardized (27 years ago), while all the other contenders (including C++!) see a major release at least every 2-3 years, and up to several times a year (for Rust).
You can't have that pace of changes and still maintain compatibility between all the different implementations.
The problem is that having multiple providers prevents the BDFL from playing too hard with the language.
If there was an alternate Python toolchain, Python3 wouldn't have happened.
Practically, PHP has one interpreter, but if they go out, you can be assured that someone will fork and maintain it.
On the other hand, if MyToyLangOnGitHubGraduateProject goes belly up, you're stuck maintaining it yourself.
What's also amazing, is that Rust is growing through sheer love of the language. There is no one pushing it, but for the joy of hacking. It is lik C in that way.
By comparison, C++ has precisely two working open source compilers --- clang and gcc --- and Rust has one: if you commit to using Rust, you're also committing yourself to an LLVM-based monoculture. The chances of the entire Rust team being simultaneously hit by a bus is low... but it's something that needs to be factored into a product assessment.