Arguably this breaks W^X. Similar implementations such as PaX prevent this. About private mappings, POSIX leaves unspecified whether changes made to the file after the mmap() call are visible in the mapped region. My basic tests show it is not visible on Linux. That said, if there's a chance for them to ever be visible somehow MDWE should also prevent it.

Proof of concept:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <fcntl.h>
#include <sys/mman.h>
#include <sys/types.h>
#include <sys/stat.h>
#include <unistd.h>
#include <errno.h>
#include <sys/prctl.h>

#ifndef PR_SET_MDWE
# define PR_SET_MDWE 65
#endif
#ifndef PR_MDWE_REFUSE_EXEC_GAIN
# define PR_MDWE_REFUSE_EXEC_GAIN 1
#endif

int main(void)
{
	int fd;
	char *addr;
	const char *data_x = "benign code";
	const char *data_X = "malicious code";
	size_t len_x = strlen(data_x);
	size_t len_X = strlen(data_X);

	// Step 0: Set MDWE to refuse EXEC gain.
	if (prctl(PR_SET_MDWE, PR_MDWE_REFUSE_EXEC_GAIN, 0, 0, 0) == -1) {
		perror("prctl(PR_SET_MDWE)");
		exit(ENOSYS);
	}

	// Step 1: Open file.
	fd = open("./mmap", O_RDWR | O_CREAT | O_TRUNC, S_IRWXU);
	if (fd == -1) {
		perror("open");
		exit(EXIT_FAILURE);
	}

	// Write initial content.
	if (write(fd, data_x, len_x) != len_x) {
		perror("write");
		exit(EXIT_FAILURE);
	}

	// Step 2: Memory-map the file.
	addr = mmap(NULL, len_x, PROT_READ | PROT_EXEC, MAP_SHARED, fd, 0);
	if (addr == MAP_FAILED) {
		perror("mmap");
		exit(EXIT_FAILURE);
	}

	// Write new content to the file.
	if (lseek(fd, 0, SEEK_SET) == -1) {
		perror("lseek");
		exit(EXIT_FAILURE);
	}

	if (write(fd, data_X, len_X) != len_X) {
		perror("write");
		exit(EXIT_FAILURE);
	}

	// Close file, this will sync the contents to the read-only memory area.
	// This breaks W^X and MDWE should prevent this.
	close(fd);

	// Check the mapped memory.
	printf("[*] Mapped Content: %s\n", addr);
	if (!strncmp(addr, "malicious", strlen("malicious"))) {
		printf("[!] RX memory updated thru a backing file write under MDWE.\n");
	}

	unlink("./mmap");
	return EXIT_SUCCESS;
}