As mentioned above, does not appear to be the option to turn on caller id blocking directly.
Played with it briefly, and appears to me that no kewl way to do it, as "*67" cannot convert to a phone number, no matter what I tried to pass that to the Call shortcut: always got "not a phone number" error.
Apologies for resurrecting this old thread, but, Apple today released v2.1.1 of Shortcuts, which now allows call numbers with # and *. So, now can take a number as input or from a Contact and prepend local caller-id blocking code.
The shortcuts can be very useful but it’s not the easiest thing to figure out. I was told by Apple tech that after the first of the year they would be putting out more examples and people could add to it