Hello. Please use the following docker image "puchuu/test_x86_64-gentoo-linux-musl". I will write here complete steps so everyone can reproduce this issue.

docker run -it puchuu/test_x86_64-gentoo-linux-musl bash
env-update && source /etc/profile
echo "dev-libs/gmp static-libs" > /etc/portage/package.use/gmp
MAKEOPTS='-j16' emerge -v dev-libs/gmp
cd /tmp && wget "https://raw.githubusercontent.com/andrew-aladev/lzws/master/cmake/checks/GMP/main.c"

gcc main.c -static -lgmp -o main && ./main
We can see that "-static -lgmp" works perfect.

gcc main.c /usr/lib/libgmp.a -o main && ./main
/usr/lib/gcc/x86_64-gentoo-linux-musl/9.2.0/../../../../x86_64-gentoo-linux-musl/bin/ld: /usr/lib/libgmp.a(bdiv_q_1.o): warning: relocation against `__gmp_binvert_limb_table' in read-only section `.text'
/usr/lib/gcc/x86_64-gentoo-linux-musl/9.2.0/../../../../x86_64-gentoo-linux-musl/bin/ld: warning: creating a DT_TEXTREL in object
Segmentation fault (core dumped)
We can see that direct usage of "/usr/lib/libgmp.a" provided DT_TEXTREL segment.

MAKEOPTS='-j16' emerge -v gdb dev-vcs/git
CFLAGS='-O0 -g -ggdb -ggdb3' CXXFLAGS='-O0 -g -ggdb -ggdb3' FEATURES='nostrip' MAKEOPTS='-j16' emerge -v musl gmp
git clone git://git.musl-libc.org/musl --depth=1 --single-branch -b "v1.1.24"
gcc -O0 -g -ggdb -ggdb3 main.c /usr/lib/libgmp.a -o main && gdb -ex=run -d musl ./main

Program received signal SIGSEGV, Segmentation fault.
0x00007fe2f8c4f231 in do_relocs (dso=0x7fe2f8c8eb40 <app>, rel=0x55af0a0cd568, rel_size=456, stride=3) at ldso/dynlink.c:423
423                             *reloc_addr = (size_t)base + addend;
(gdb) where
#0  0x00007fe2f8c4f231 in do_relocs (dso=0x7fe2f8c8eb40 <app>, rel=0x55af0a0cd568, rel_size=456, stride=3) at ldso/dynlink.c:423
#1  0x00007fe2f8c51e60 in reloc_all (p=0x7fe2f8c8eb40 <app>) at ldso/dynlink.c:1328
#2  0x00007fe2f8c53a03 in __dls3 (sp=0x7ffc82457260) at ldso/dynlink.c:1906
#3  0x00007fe2f8c52de6 in __dls2b (sp=0x7ffc82457260) at ldso/dynlink.c:1672
#4  0x00007fe2f8c52d4e in __dls2 (base=0x7fe2f8bba000 "\177ELF\002\001\001", sp=0x7ffc82457260) at ldso/dynlink.c:1650
#5  0x00007fe2f8c4e5a0 in _dlstart_c (sp=0x7ffc82457260, dynv=0x7fe2f8c8be20) at ldso/dlstart.c:147
#6  0x00007fe2f8c4e246 in _dlstart () from /lib/ld-musl-x86_64.so.1
#7  0x0000000000000001 in ?? ()
#8  0x00007ffc82458635 in ?? ()
#9  0x0000000000000000 in ?? ()

(gdb) info locals
base = 0x561041462000 "\177ELF\002\001\001"
syms = 0x5610414622c8
strings = 0x561041462478 ""
sym = 0x0
name = 0x5610414624f8 "free"
ctx = 0x7f9eea640b40 <app>
type = 8
sym_index = 0
def = {sym = 0x0, dso = 0x7f9eea640b40 <app>}
reloc_addr = 0x56104147cf79 <__gmpn_bdiv_q_1+25>
sym_val = 0
tls_val = 0
addend = 131264
skip_relative = 0
reuse_addends = 0
save_slot = 0

(gdb) p laddr(dso, rel[0])
$27 = (void *) 0x56104147cf79 <__gmpn_bdiv_q_1+25>

(gdb) p dso->loadmap
$28 = (struct fdpic_loadmap *) 0x0

(gdb) p (dso->base + rel[0])
$29 = (unsigned char *) 0x56104147cf79 <__gmpn_bdiv_q_1+25> "\300"

We can see that "laddr" provided pointer to "dso->base + rel[0]", than switch tried to override it's value and segfault appeared. Pointer is wrong, most likely readonly.

You can replace "gcc" with "clang" and everything will be the same. Updated binutils to most recent version 2.33.1 and rebuilt toolchain - nothing changed. Pointer is still invalid and SEGV_ACCERR appears.

So I think that bug is inside musl itself. Glibc container is the same situation works fine. I see no way to create a workaround for this issue.