Currently, unincorporated status for census places can be found using the NHGIS data finder tool for 1970 and 1980. There is no separate variable for it. Rather, status is indicated in the place name. Unincorporated place names for 1970 will have a “(U)” after the name to indicate that they are unincorporated. For 1980, unincorporated place names will be followed by a "CDP ‘’ for census-designated place. You want to make sure to select “Place (by State)” and one of the mentioned decennial years in the data finder tool. You will need to also select a source table to proceed to the extract, though any source table (such as total population) will work.
I did some looking on the census website for the other years you had mentioned and found scans of census tables from 1950 and 1960 that indicate incorporated status. IPUMS has not digitized these and I’m not aware if anyone else has.
Hope that helps!