Buttigieg would probably throw trans people under the bus to make a deal, but he seems against it generally ... the problem with overly pragmatic politicians is you can't tell how far they will sacrifice their values in the name of pragmatism. The extreme end of this is that don't really have any values - and sometimes this is exactly how Buttigeg comes across (as overly eager to win, and willing to mold himself and do whatever it takes).
He has repeated transphobic talking points about trans exclusion in sports, which I take to mean he is trying to position himself as a moderate. (Which makes sense, in this same interview he mentions Sarah McBride is a major influence or someone he sees shared values with - she has also advocated for Democrats capitulating and endorsing transphobic policies in the name of political pragmatism and keeping a big tent.)