The latter: Tenir des propos is an idiom that means to openly tell something.
It is slightly formal. It is usually followed by an adjective qualifying the expressed statements, e.g.:
Il tient des propos joyeux/intelligents/incohérents/racistes/injurieux/surprenants/sensés/...
Here, de tels propos means words that would clearly reveal the speaker's lack of knowledge about politics.
While a common meaning for tenir is "to hold", it has a much wider range of usage like its latin ancestor tenēre, as much as sixty nine according to wikipedia. See also the dictionnaire de l'académie.
Propos means statements here.