While I did find similar-ish questions, they did not really answer this specific question.
Can a compiled x86 executable run on any x86 platform given the right runtime libraries? Say I make a C++17 program without dependencies, could I run this program on Windows 95 or is there some sort of support required by the OS?
I also heard that RTTI (in the case of C++) may not be supported everywhere, is this only due to the processor having to support this feature or does the OS play a role in that? This would imply that new features would maybe not be supported by, e.g., Windows 95.
What I'm after is whether an executable (e.g., x86) can run on any platform supporting that instruction set or wether certain features, like RTTI, need specific OS support and thus are not available on all platforms supporting that instruction set.
In general you cannot, even if you restricted your universe to x86 hardware - at least not without some conversion of the binary or some platform-specific "loader" for each target platform.
For exmaple a typical binary emitted by a C or C++ compiler1 will have some minimal dependency on the OS and runtime, for example to load and do runtime linking on the executable. Different platforms have different binary formats (such as PE/COFF on Windows or ELF across various UNIX flavors and Linux) and there isn't any common "x86 format" that would work directly on any platform.
Furthermore, any non-trivial program and in many cases any program, trivial or not, is going to have platform-specific dependencies on the the langauge runtime. For example, even an empty main() function often requires runtime support to get from the OS-defined "start" method to the main method, and without unusual build options there are often calls at startup to initialize parts of the standard library.
Finally, as you alluded to with your comment about RTTI, various language or platform features may essentially be compiled into the binary and require OS support. RTTI probably doesn't obviously fall into this category, but things like position-independent code, thread-local storage and stack-unwinding support for exception handling often do. The compiled x86 code that uses such features may be quite different on different platforms since it needs to build in assumptions of how those work.
In principle, however, you could imagine this working, at least for some limited subset of programs. For example, while the various executable formats are in practice incompatible, they aren't that different and tools exist to convert between them. So you could certainly implement a minimal runtime on your platform of interest that takes an x86 executable compiled to whatever fixed format you choose and converts at runtime to the local format and runs it.
Beyond that actually trying to map even standard library calls would be quite difficult since different operating systems using different calling conventions, but it could be possible for "C" functions using some thunks to put things in the right place. C++ is pretty much right out because the ABI there is much more complex, compiler-and-platform specific and much of the implementation detail is already compiled-in for stuff implemented in headers.
In fact, the idea that (a subset of) x86 might provide a interesting intermediate language for cross-platform execution is exactly the idea behind exploited in Google's [NaCl project]. Essentially, the NaCl runtime provides platform agnostic "loading" capabilities which allow x86 code to run more-or-less natively on various platforms. Subsequently other native formats such as ARM were added, but it started as an x86 sandbox. A large part of the project deals with running code that provably safe (i.e., sandboxed) - but it shows that with some infrastructure you can write "portable" x86. A standard C or C++ compiler isn't going to emit NaCl compatible code directly, however.
1 Really, any compiler that compiles to a native format. I just call out C and C++ since they seem like the ones you are interested in and are widely familiar.