C vs C++ compilation incompatibility - does not name a type

I am trying to use a supplier's library in combination with my C++ application. The library is largely based on C, which is normally not a problem with the `extern "C"` option, but I ran into an issue that the C++ compiler does not accept.

I simplified my code into the following example files. header.h represents a header from the suppier library, main.c/cpp are my own files. My real application is a C++ application, so I want to get it to work with main.cpp.

header.h (note the line `u64 u64;`):

#ifndef HEADER_H
#define HEADER_H

#include <stdint.h>

typedef uint64_t u64;

union teststruct {
u64 u64;
struct {
u64 x:32;
u64 y:32;
} s;
};

#endif

main.c:

#include <stdio.h>
#include "header.h"

int main() {
union teststruct a;
a.u64=5;
printf("%x\n", a.u64);

return 0;
}

main.cpp (same as main.c but with an extra `extern "C"` statement):

#include <stdio.h>

extern "C" {
#include "header.h"
}

int main() {
union teststruct a;
a.u64=5;
printf("%x\n", a.u64);

return 0;
}

Compiling main.c using the line

gcc -o test main.c

compiles without problems. However, compiling the C++ version using the g++ compiler with the command

g++ -o test main.cpp

gives the following compiler errors:

In file included from main.cpp:12:0:
header.h:11:9: error: ‘u64’ does not name a type
u64 x:32;
^
header.h:12:9: error: ‘u64’ does not name a type
u64 y:32;
^

The issue is that the supplier used the same name (u64) for both the type and the variable name, which seems like a bad idea to begin with, but gcc apparently accepts it. I do not want to change the library (i.e. header.h) as it is very large,this occurs a lot in the code, and I occasionally get updates for it. Is there a way to make g++ accept this combination, or a way to modify main.cpp to make it compile _without_ changing header.h?