As an example, Strawberry Perl has binutils-2.32 and MSYS2 has binutils 2.30-1

I avoid having a gcc toolchain installed on MSYS2.
If I need a compiler inside MSYS2's msys2_shell.cmd shell (as is often the case), I use a mingw-w64 port of gcc (eg the one provided by Strawberry Perl).
I was thinking you'd be using MSYS2 mainly for git, but it's also handy for building C/C++ libraries and for providing 3rd party libraries - eg Gtk2/Gtk3/Gnome, that can be utilized to build the Gtk2/Gtk3/Gnome perl modules on Win32 perls (including Strawberry Perl).

I've been doing that sort of stuff for so long now that I had quite forgotten that mixing Strawberry Perl and MSYS2 can also be a bit tricky.
Thanks to xiaoyafeng for reminding me that one has to be a little mindful of how the path is set on those occasions when both MSYS2 and Strawberry Perl environments need to intersect.
It's hard to come up with a general plan to cover all eventualities, but I think a good start is to set things up so that the default Windows path includes neither MSYS2 nor Strawberry Perl. Then you can just bring in bits and pieces of each, as needed for the particular task.

Cheers,
Rob