The following code is not constant-time.

#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>

typedef uint8_t(* issue_t)(const uint32_t, const uint8_t, const uint8_t);

uint8_t issue(const uint32_t c, const uint8_t a, const uint8_t b) {
  if(c) {
    return a;
  }
  else {
    return b;
  }
}

int main(int argc, char *argv[]) {
  uint32_t a = 2, b = 5, c = 0;
  // c is our secret value, we read its content from the environment so the 
  // compiler cannot play tricks on us by inlining
  if (argc >= 2) {
    c = (uint32_t) strtol(argv[1], NULL, 16);
  }
  else {
    fprintf(stderr, "USAGE: %s hex_value\n", argv[0]);
    return 1;
  }
  // declarations and markup here
  
  volatile issue_t func = issue;
  printf("%d\n", func(c, a, b));

  return 0;
}

See the compilation results with different optimization levels on GodBolt.