It is undeniable that footballers have, on average, grown as the population has in the years following the recovery from World War II, but that does not mean there were not people [and players] who were of above average height even in the 19th Century. As a result of this, some of these players probably only got a match because they were tall and had stood out [metaphorically] in juvenile football.
Height Name Position 6' 3" Thomas Bellingham CF 1885/86-1887/88 6' 2½" Duncan Elliot GK 1897/98 6' ½" James Strathie RB 1933/34-1934/35 6' George Brewster OR 1918/19 6' William Brown RH 1937/38-1941/42 6' Robert Wilson GK 1938/39-1940/41 5' 11" William Raisbeck LH 1905/06-1906/07 5' 11" Stephen MacDonald RH 1909/10-1916/17 5' 11" John Robertson LH 1913/14 5' 11" Joseph Whitton GK 1927/28 5' 11" James McNair IL 1933/34-1935/36 5' 11" Kenneth Dawson OL 1934/35-1950/51 5' 11" Gilbert McKie GK 1936/37-1942/43 5' 11" Alex Allan IR 1937/38-1938/39I have included the heights of the following players who were measured within an inch of the above, for the simple fact that I do not completely trust the accuracy of imperial measurements, and it is never clear whether they rounded up or down throughout the 50+ years I have researched.
5' 10½" John Morrison CH 1906/07-1915/16 5' 10½" Thomas Logan CF 1910/11-1912/13 5' 10" Joseph McQue CH 1898/99 5' 10" Alex Stewart GK 1908/09-1916/17 * 5' 10" Frank Reilly LH 1912/13/1919/20 5' 10" Thomas Ferguson GK 1918/19-1931/32 5' 10" Daniel Thomson CF 1921/22-1922/23 5' 10" Patrick Docherty LH 1934/35-1935/36 5' 10" Edwin Young OL 1938/39 5' 10" William Miller IL 1938/39-1941/42 5' 10" Alex Stewart CF 1938/39-1942/43 * 5' 10" Henry Pinkerton LH 1938/39-1945/46* The two Alex Stewarts were Father & Son.
NB - It says on his wikipedia page that Jock Drummond was 5' 10" but has no supporting evidence, so I have left it out.