Baur had been a member of the SPD since 1911. In 1946 he became district chairman of his party in Swabia and was a member of the party executive committee from 1946 to 1949.
From December 1946 to June 1947, Baur was a member of the state parliament in Bavaria. From 1947 to 1949 Baur was a member of the Economic Council. From 1949 to 1961 he was a member of the German Bundestag. He represented the Augsburg constituency in the Bundestag.
Herbst, Ludolf; Jahn, Bruno (2002). Vierhaus, Rudolf (ed.). Biographisches Handbuch der Mitglieder des Deutschen Bundestages. 1949–2002 [Biographical Handbook of the Members of the German Bundestag. 1949–2002] (in German). München: De Gruyter - De Gruyter Saur. p. 1715. ISBN978-3-11-184511-1.
Dorls (from 13 December 1950 WAV-Gast, from 17 January 1951 WAV, from 26 September 1951 Non-attached, am 23 October 1952 Mandatsaberkennung)
Frommhold (from 7 September 1949 Nationale Rechte, from 5 October 1950 Non-attached (DRP), from 26 March 1952 DP-Gast, from 11 February 1953 Non-attached)
Miessner (from 5 October 1950 FDP-Gast, from 20 December 1950 FDP)
Rößler (from 15 September 1949 Nationale Rechte, from 6 September 1950 Non-attached, from 13 December 1950 WAV-Gast, from 17 January 1951 WAV, from 26 September 1951 Non-attached, until 21 February 1952)
Thadden (from 15 September 1949 Nationale Rechte; 1950 DRP, from 20 April 1950 Non-attached)
Ott (Non-attached, from 4 May 1950 WAV-Gast, from 13 October 1950 BHE/DG, from 21 March 1952 Non-attached, from 26 March 1952 DP/DPB-Gast, from 26 June 1952 Non-attached)
Berg (from 27 June 1955, from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Blank (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Blücher (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Euler (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Fassbender (from 18 November 1955 DP, from 14 March 1957 DP/FVP)
Hübner (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Manteuffel (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Neumayer (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Preiß (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Preusker (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Schäfer (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Schneider (from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Bender (from 12 July 1955 Non-attached, from 14 July 1955 Group Kraft/Oberländer, from 15 July 1955 Guest of CDU/CSU-Fraktion, from 20 March 1956 CDU/CSU)
Eckhardt (from 12 July 1955 Non-attached, from 14 July 1955 Group Kraft/Oberländer, from 15 July 1955 Guest of CDU/CSU-Fraktion, from 20 March 1956 CDU/CSU)
Finck (from 12 July 1955 Non-attached, from 14 July 1955 Group Kraft/Oberländer, from 15 July 1955 Guest of CDU/CSU-Fraktion, from 20 March 1956 CDU/CSU)
Haasler (from 12 July 1955 Non-attached, from 14 July 1955 Group Kraft/Oberländer, from 15 July 1955 Guest of CDU/CSU-Fraktion, from 20 March 1956 CDU/CSU)
Körner (from 12 July 1955 Non-attached, from 14 July 1955 FDP, from 23 February 1956 Non-attached, from 15 March 1956 Demokratische Arbeitsgemeinschaft (DA), from 26 June 1956 FVP, from 14 March 1957 DP/FVP)
Kraft (from 12 July 1955 Non-attached, from 14 July 1955 Group Kraft/Oberländer, from 15 July 1955 Guest of CDU/CSU-Fraktion, from 20 March 1956 CDU/CSU)
Oberländer (from 12 July 1955 Non-attached, from 14 July 1955 Group Kraft/Oberländer, from 15 July 1955 Guest of CDU/CSU-Fraktion, from 20 March 1956 CDU/CSU)
Samwer (from 15 October 1953, from 12 July 1955 Non-attached, from 14 July 1955 Group Kraft/Oberländer, from 15 July 1955 Guest of CDU/CSU-Fraktion, from 20 March 1956 CDU/CSU)
