The problem with the statement "choose a different coordinator" is that there are to date, as far as I am aware, no other coordinators to choose from. And sure, you can spin up your own, but if it is only you and one or two other people using it, then the anonymity it provides is easily broken. People who are using Wasabi aren't generally going to bother changing coordinator, because anyone who actually cares about privacy and not having their details fed directly to a blockchain analysis firm isn't using Wasabi in the first place.
Are these claims true? How can a privacy-enhancing service provide data to parties trying to reveal identity?
Because they care about their lining their own pockets more than they care about the privacy of their users.