Users don’t currently have any control over how Airtable’s webhook automation trigger responds to requests (and I doubt that we ever will). I recommend reaching out to Airtable support directly (in the app: Help → Contact support). While Airtable staffers do frequent the forum, they prefer to be approached directly with support requests, and this leans pretty heavily in that direction IMO.
That aside, have you tried the “no-cors” mode that was recommended in the error message you received (seen in your screenshot)? I’ve only called Airtable webhooks from within other Airtable scripts, so I haven’t needed to test this workaround and therefore don’t know how exactly it should be applied, but it’s probably worth investigating.