During the Ruusan Reformations, the following reforms were enacted:
In order to lessen the chance of a Sith resurgence, the Order began training children from birth. In addition, the training of Padawans was centralized on Coruscant, to remove the danger of unsupervised students delving into forbidden Sith knowledge.
The measures are intended to prevent Force sensitives from learning the ways of the dark side. Setting a cut-off age for inducting untrained Force sensitives into the Jedi Order seems to run counter to the goal here: untrained, unsupervised Force sensitives are believed to be more susceptible to the dark side.
So why the contradiction? It can't be sentient rights, not when you can legally take newborns from their parents.