For birding the 1DX noisy shutter would easily scare many species even in the so-called silent mode. It's a big deal and one thing less to try and work around with cameras like the A9. If they had a silent mode as least as quiet as the 5D4's it would be a decent compromise if you could still shoot at say 5-7fps.
It's not a big deal. Birders have used the 'noisy' 1dx and Nikon D's for the last decade in the field and come back with amazing, world class images. Silent shooting is frankly overrated for most wildlife photography. Most of the time wildlife is already aware of the presence of humans and tolerate it as long as you're far enough. Hence the use of 600's, 1.4 TC and 2x TC.