I don't think this is true. Loads of FP languages are self-hosted.

Not only FP. Lots of languages are self-hosted. So actually most modern parsers are not written in C, since they are written in the language they parse.

Probably true, but only because the implementation language for them is also C. Some of them also frequently use a mix of the implementation language and grammar specification DSL like yacc.

Use of DSLs and tools like flex and bison makes the implementation a whole lot more reliable (but only if they're used, and some commonly run languages have a very implementation-specific grammar).

consider:

    input:    /* empty string */
            | input line
    ;
    
    line:     '\n'
            | exp '\n'  { printf ("\t%.10g\n", $1); }
    ;
    
    exp:      NUM                { $$ = $1;         }
            | exp '+' exp        { $$ = $1 + $3;    }
            | exp '-' exp        { $$ = $1 - $3;    }
            | exp '*' exp        { $$ = $1 * $3;    }
            | exp '/' exp        { $$ = $1 / $3;    }
            | '-' exp  %prec NEG { $$ = -$2;        }
            | exp '^' exp        { $$ = pow ($1, $3); }
            | '(' exp ')'        { $$ = $2;         }
    ;

http://dinosaur.compilertools.net/bison/bison_5.html#SEC27

Python, Ruby, PHP: C

JS: no standard parser, but V8(chrome), SpiderMonkey(firefox) and Chakra(edge) are all C++

Go, C, C++: self-hosted (written in the same language)

Java, Erlang: parser/compiler self-hosted, but VMs written in C.

I doubt it. If anything, C++, but even that doesn't seem likely. The vast majority of languages seem to be self-hosted. A good portion compilers or interpreters in C or C++ probably use (F)lex and Yacc/Bison so even saying C or C++ are the most popular choice (but not necessarily the majority) sounds like a stretch.

Go is now written in Go

It used to be written in C before bootstrapping.