Statically linking libc into my binary causes it to segfault

I need to build a binary with libc statically linked. I have libc.a available in the same directory as the source code. To compile, I tried the following:

gcc -o foo foo.c libc.a 

This resulted in the following issue:

/usr/bin/ld: dynamic STT_GNU_IFUNC symbol `strcmp' with pointer equality in `libc.a(strcmp.o)' can not be used when making an executable

In researching this, I found the following question: Linking partially static and partially dynamic in GCC

Following the solution in the top answer, I created my own string comparison function in my_strcmp.c and tried the following compilation:

gcc -o foo foo.c mystrcmp.c libc.a 

And it works, but the binary now segfaults quite early. This doesn't happen without libc statically linked. Here's the GDB trace:

(gdb) backtrace                                
#0  0x00000000004fe48e in generic_start_main ()
#1  0x00000000004fe891 in __libc_start_main () 
#2  0x0000000000406b56 in _start ()  

Not really sure how to interpret this. Anyone have any ideas?