I don't think AT&T is pulling their basic cable channels (e.g. CNN, TBS, TNT) from any streaming cable TV packages, whether that's Hulu Live or YTTV or anyone else.
Also, they have not announced anything about HBO Max including any live linear channels at launch. (I think there's a decent chance it will include at least the original linear HBO channel but that's just my hunch. I very much doubt it will include the live channels of CNN, TBS, etc.). Now, by next year, HBO Max is supposed to offer one or more add-on live cable channel bundles, the same way that Hulu does. I'm sure those bundles will include all of AT&T's own channels, as well as channels from other companies too. (I believe those bundles will simply be repeats of what they also sell under the AT&T TV brand.)
What IS going on right now is that AT&T is pulling at least *some* of the WarnerMedia content they own from competing on-demand streaming services like Netflix and Hulu so that it will exclusively reside in HBO Max's on-demand library. The highest-profile examples of that include Friends and The West Wing.