Where can one (realistically, not in theory) teach at a University (as a tenure-track professor) without a PhD? (Straight out of graduate school at a U.S. institution)
Technically, universities hire MFAs and similar terminal, non-doctoral degrees into tenure track positions, but I don't think these are degrees you're talking about.
So, what universities will hire people without terminal degrees?
A university that cannot find people with PhDs to fill tenure track positions.
Historically (even as recently as the 1960s and 70s based upon the older faculty at my undergraduate university), many universities in the United States did not require PhDs to be on faculty, only an MS degree.
As the number of PhD increased, these hires became increasingly rare.
At the present, some small liberal arts universities might hire tenure track faculty without PhDs and community and technical colleges will hire people without PhDs, if they are good at teaching.
Some of these positions are tenure track like.
Likewise, professors of practice do not always need a PhD, but these positions require professional experience (something the Straight out of graduate school at a U.S. institution seems to suggest you do not have).
I think your key limitation is "Straight out of graduate school at a U.S. institution.