No, there is nothing preventing interoperability.
The main reason (this is an opinion, not based on known facts) that Fortran seems to have more interop out-of-the-box was that there was a free software GNU/Fortran for interested parties to work with. COBOL was very late in the game getting a viable free software compiler. That is no longer an issue with GnuCOBOL and people are finally starting to write the code needed to catch up.
Adding to Simon's answer; proof of concept for direct embedding is in a branch for GnuCOBOL; intrinsic functions added to support FUNCTION TCL, FUNCTION PYTHON, FUNCTION REXX, FUNCION LUA and FUNCTION JVM, so far. With FUNCTION JVM tests for Scala, Groovy, Java, Frink, all worked. This allows data transfer between COBOL working storage and the other language engine using simple COBOL syntax. Including setups for callbacks to and from. Those functions are embedded into the compiler and libcob run-time, when using that branch.
For other interface trials, not built into the compiler, but still allowing interop; the GnuCOBOL FAQ has dozens of examples. Shakespeare? Yep. Falcon? Yep. C, well, GnuCOBOL emits intermediate C so that's covered in spades. There is also a C++ edition of the compiler, so C++ is also covered, in spades. Javascript; Jsish, Duktape, Spidermonkey, Quickjs to name a few of the trials.
Ada, D, Vala, Genie, S-Lang, ROOT/CINT, J, Gambas, Forth, Perl, Postscript, Pure, Icon and Unicon, Nim, BaCon, SWIG (which opens up many multiples), PARI/GP, Gretl, R, Red, Ruby, Haxe/Neko, Pascal, Erlang, Elixir, SQLite, Rust, Go, more..., including a fair number of esolangs, and GNU Lightning for on the fly assembly modules. Trials documented in the GnuCOBOL FAQ.
Framework interfacing for AWT/Swing, GTK, Agar, and things like ZeroMQ, CGI and websockets also proved successful and are in productive use. Along with at least 7 EXEC SQL preprocessors successfully tested, and in use.
It comes down to someone caring to try, and writing some glue or properly aligning call frames. No attempts I've tried have failed to produce satisfactory results, although Perl 5 was a hair pull of unraveling macro layers. (Ok, I just lied, while attempting to embed jq, which relies on using C call and return by struct features, I would have had to leave pure COBOL interface coding, and didn't bother with the C middleware that would have made it easy). ;-) Will do that someday though, as jq is quite the powerful little JSON handler.
Use the search engine you mistrust the least and look for "gnu-cobol-builtin-script" and "GnuCOBOL FAQ", and visit the hits on SourceForge.
In my particular explorations I usually focus on languages with a C Application Binary Interface, but other ABIs would be along a similar vein. It only takes sitting down and writing some middleware or figuring out how to properly synch the call frames.
Are these current samples perfect? Not always, there are edge and corner cases with some datatypes and COBOL PICTURE data that would require more work, but that is all; a little bit of work and testing to smooth over the bumps. When exploring, I don't always go that far until an actual need arises. These seed work experiments are just to get some proof in the pudding, all done for the simple joy of it.
One of the lead developers for GnuCOBOL just added uni and bi-directional piping using simple filenames, which provides access to whatever the base OS offers, using basic COBOL OPEN/READ/WRITE/CLOSE (and other file IO) statements. Code was committed to trunk just a few hours before I started typing this response.
Basically, the answer to the titular question is a resounding No.
