Build fails on MinGW toolchain

When building this crate with a Windows MinGW toolchain and the default features, the build fails with the following error:
2020-10-21T21:29:29.6706562Z The following warnings were emitted during compilation:
2020-10-21T21:29:29.6713138Z 
2020-10-21T21:29:29.6715262Z warning: C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S: Assembler messages:
2020-10-21T21:29:29.6717108Z warning: C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:125: Error: unknown pseudo-op: `.hidden'
2020-10-21T21:29:29.6719003Z warning: C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:125: Warning: .type pseudo-op used outside of .def/.endef: ignored.
2020-10-21T21:29:29.6720960Z warning: C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:125: Error: junk at end of line, first unrecognized character is `c'
2020-10-21T21:29:29.6723058Z warning: C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:266: Warning: .size pseudo-op used outside of .def/.endef: ignored.
2020-10-21T21:29:29.6725003Z warning: C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:266: Error: junk at end of line, first unrecognized character is `c'
2020-10-21T21:29:29.6726011Z 
2020-10-21T21:29:29.6726512Z error: failed to run custom build command for `cloudflare-zlib-sys v0.2.0`
2020-10-21T21:29:29.6726966Z 
2020-10-21T21:29:29.6727202Z Caused by:
2020-10-21T21:29:29.6728208Z   process didn't exit successfully: `D:\a\project\project\target\release\build\cloudflare-zlib-sys-73a788ab2f5bd751\build-script-build` (exit code: 1)
2020-10-21T21:29:29.6729186Z   --- stdout
2020-10-21T21:29:29.6729444Z   OPT_LEVEL = Some("3")
2020-10-21T21:29:29.6729817Z   TARGET = Some("x86_64-pc-windows-gnu")
2020-10-21T21:29:29.6730252Z   HOST = Some("x86_64-pc-windows-msvc")
2020-10-21T21:29:29.6730669Z   CC_x86_64-pc-windows-gnu = None
2020-10-21T21:29:29.6731034Z   CC_x86_64_pc_windows_gnu = None
2020-10-21T21:29:29.6731343Z   TARGET_CC = None
2020-10-21T21:29:29.6731607Z   CC = None
2020-10-21T21:29:29.6731937Z   CFLAGS_x86_64-pc-windows-gnu = None
2020-10-21T21:29:29.6732305Z   CFLAGS_x86_64_pc_windows_gnu = None
2020-10-21T21:29:29.6732672Z   TARGET_CFLAGS = None
2020-10-21T21:29:29.6733085Z   CFLAGS = None
2020-10-21T21:29:29.6733401Z   CRATE_CC_NO_DEFAULTS = None
2020-10-21T21:29:29.6733730Z   DEBUG = Some("false")
2020-10-21T21:29:29.6734144Z   CARGO_CFG_TARGET_FEATURE = Some("fxsr,sse,sse2")
2020-10-21T21:29:29.6735090Z   cargo:include=C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor
2020-10-21T21:29:29.6735965Z   CC_x86_64-pc-windows-gnu = None
2020-10-21T21:29:29.6736305Z   CC_x86_64_pc_windows_gnu = None
2020-10-21T21:29:29.6736614Z   TARGET_CC = None
2020-10-21T21:29:29.6736875Z   CC = None
2020-10-21T21:29:29.6737213Z   CFLAGS_x86_64-pc-windows-gnu = None
2020-10-21T21:29:29.6737604Z   CFLAGS_x86_64_pc_windows_gnu = None
2020-10-21T21:29:29.6737949Z   TARGET_CFLAGS = None
2020-10-21T21:29:29.6738247Z   CFLAGS = None
2020-10-21T21:29:29.6738535Z   CRATE_CC_NO_DEFAULTS = None
2020-10-21T21:29:29.6738966Z   CARGO_CFG_TARGET_FEATURE = Some("fxsr,sse,sse2")
2020-10-21T21:29:29.6739411Z   CC_x86_64-pc-windows-gnu = None
2020-10-21T21:29:29.6739773Z   CC_x86_64_pc_windows_gnu = None
2020-10-21T21:29:29.6740078Z   TARGET_CC = None
2020-10-21T21:29:29.6740338Z   CC = None
2020-10-21T21:29:29.6740671Z   CFLAGS_x86_64-pc-windows-gnu = None
2020-10-21T21:29:29.6741061Z   CFLAGS_x86_64_pc_windows_gnu = None
2020-10-21T21:29:29.6741377Z   TARGET_CFLAGS = None
2020-10-21T21:29:29.6741667Z   CFLAGS = None
2020-10-21T21:29:29.6741979Z   CRATE_CC_NO_DEFAULTS = None
2020-10-21T21:29:29.6742440Z   CARGO_CFG_TARGET_FEATURE = Some("fxsr,sse,sse2")
2020-10-21T21:29:29.6745332Z   running: "gcc.exe" "-O3" "-ffunction-sections" "-fdata-sections" "-fPIC" "-m64" "-I" "C:\\Users\\runneradmin\\.cargo\\registry\\src\\github.com-1ecc6299db9ec823\\cloudflare-zlib-sys-0.2.0\\vendor" "-mpclmul" "-msse4.2" "-msse4.2" "-DHAVE_OFF64_T=1" "-D_LARGEFILE64_SOURCE=1" "-DHAVE_UNISTD_H=1" "-DHAS_PCLMUL" "-DHAS_SSE42" "-DHAVE_HIDDEN=1" "-o" "D:\\a\\project\\project\\target\\x86_64-pc-windows-gnu\\release\\build\\cloudflare-zlib-sys-3592ede97c492f3c\\out\\crc32-pclmul_asm.o" "-c" "C:\\Users\\runneradmin\\.cargo\\registry\\src\\github.com-1ecc6299db9ec823\\cloudflare-zlib-sys-0.2.0\\vendor\\contrib/amd64/crc32-pclmul_asm.S"
2020-10-21T21:29:29.6748727Z   cargo:warning=C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S: Assembler messages:
2020-10-21T21:29:29.6750496Z   cargo:warning=C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:125: Error: unknown pseudo-op: `.hidden'
2020-10-21T21:29:29.6752370Z   cargo:warning=C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:125: Warning: .type pseudo-op used outside of .def/.endef: ignored.
2020-10-21T21:29:29.6754353Z   cargo:warning=C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:125: Error: junk at end of line, first unrecognized character is `c'
2020-10-21T21:29:29.6756291Z   cargo:warning=C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:266: Warning: .size pseudo-op used outside of .def/.endef: ignored.
2020-10-21T21:29:29.6758227Z   cargo:warning=C:\Users\runneradmin\.cargo\registry\src\github.com-1ecc6299db9ec823\cloudflare-zlib-sys-0.2.0\vendor\contrib/amd64/crc32-pclmul_asm.S:266: Error: junk at end of line, first unrecognized character is `c'
2020-10-21T21:29:29.6759322Z   exit code: 1
2020-10-21T21:29:29.6759500Z 
2020-10-21T21:29:29.6759733Z   --- stderr
2020-10-21T21:29:29.6759925Z 
2020-10-21T21:29:29.6760074Z 
2020-10-21T21:29:29.6763079Z   error occurred: Command "gcc.exe" "-O3" "-ffunction-sections" "-fdata-sections" "-fPIC" "-m64" "-I" "C:\\Users\\runneradmin\\.cargo\\registry\\src\\github.com-1ecc6299db9ec823\\cloudflare-zlib-sys-0.2.0\\vendor" "-mpclmul" "-msse4.2" "-msse4.2" "-DHAVE_OFF64_T=1" "-D_LARGEFILE64_SOURCE=1" "-DHAVE_UNISTD_H=1" "-DHAS_PCLMUL" "-DHAS_SSE42" "-DHAVE_HIDDEN=1" "-o" "D:\\a\\project\\project\\target\\x86_64-pc-windows-gnu\\release\\build\\cloudflare-zlib-sys-3592ede97c492f3c\\out\\crc32-pclmul_asm.o" "-c" "C:\\Users\\runneradmin\\.cargo\\registry\\src\\github.com-1ecc6299db9ec823\\cloudflare-zlib-sys-0.2.0\\vendor\\contrib/amd64/crc32-pclmul_asm.S" with args "gcc.exe" did not execute successfully (status code exit code: 1).
This error also has an unanswered StackOverflow question about it, so I'd say I'm not the only one experiencing it.
Building with a MSVC toolchain works, but then another dependency of my Rust project fails to compile a component I need for the application to work completely, so switching the toolchain is not a solution for me. Also, I wish I wouldn't need to just drop or degrade Windows compatibility.
I'd appreciate any tips about the cause of this (for me rather cryptic) error and how it can be fixed. Thanks!
Edited Oct 23, 2020 by Alejandro González