Google actually did and does a whole lot to support firefox security. There's a lot of collaboration in the security space, e.g. Firefox and Chrome security tea

Google actually did and does a whole lot to support firefox security. There's a lot of collaboration in the security space, e.g. Firefox and Chrome security teams heavily collaborate on fixing the TLS/CA ecosystem. Also the interest is very often shared, because a whole pile of libraries are used by both browsers: freetype, libjpeg-turbo, libpng, giflib, expat, webrtc, opus, ...