Since you were dealing with a birth from 1910, you could have used the Vienna addressbooks, which are online for 1859 to 1941 at https://www.digital.wienbibliothek.at/wbrobv/periodical/titleinfo/5311. This is somewhat tricky to use, but with some practice can be quite useful.
Going to the 1910 volume (click on the year number, not the PDF, which is huge) gets you to this: https://www.digital.wienbibliothek.at/wbrobv/periodical/titleinfo/230383. Band 2 has the name index; clicking through that to the "Namensverzeichnis" gets you this page, which has 7 entries for Hintereggers, with their street addresses (as well as the district number).
Now if you open up again the general page for the 1910 volume (https://www.digital.wienbibliothek.at/wbrobv/periodical/titleinfo/230383) in a separate window, go to Band 1, which has a street index (Straßenverzeichnis) here . Note that it has both "Straßen in den einundzwanzig Gemeinde-Bezirken" and a list of the "Katholische Pfarren".
The first Hinteregger, Alois, lived in Margarethenstr. 151. If you look in the "Straßen in den einundzwanzig Gemeinde-Bezirken" here, you will see that odd street numbers 51 and above are in parish 21, which, by reference to the parish list at https://www.digital.wienbibliothek.at/wbrobv/periodical/pageview/125327) is St. Josef in Margarethen.
Repeating this process for the next Hinteregger, Anton, who lived in Goldschlagstr. 98 in District XIV/1, you will see here that that is in parish 49, which per the parish list is the parish Zum heiligen Rudolph in Rudolfsheim (which is indeed where you found your guy).
These address books will be a valuable resource for tracing the father, his job titles over time, his addresses over time, and when he first and last appeared in Vienna.
