This is an extremely complicated question, but I can provide two starting points and sources for further study.
There is some evidence that Herakles was connected with the Peisistratid regime at Athens, and that the aristocratic Athenian families (the Alkmaionidai in particular) began to cultivate Theseus as a 'replacement' hero after the fall of the last tyrant late in the 6th century BCE. There is a theory that Kleisthenes, one of the important figures in the initiation of democracy at Athens, actually composed the (now lost) Theseis, possibly working from an older, defunct epic centered on Theseus. Indeed only a generation or two later, in the early years of the Delian League, we find Bacchylides devoting several poems to Theseus topics as well. The center of this answer lies in aristocratic "patronage" of Theseus as a digestible replacement for Herakles, who had become tangled up in the ideology of the tyrants. This patronage would have included artistic commissions on ceramics and sculpture as well as literary initiative. Note that the metope sculptures on the Athenian treasury at Delphi are shared between Theseus and Herakles. For a good and short discussion of all this (though it is dated), see John Boardman, "Herakles, Peisistratos and Eleusis," Journal of Hellenic Studies 1975: 1-12.
Theseus as a political symbol is closely associated with the democracy at Athens. Already in the "Theseus Cups" we find a few examples of Theseus in the identical pose of Harmodius, the tyrannicide; after the Persian Wars, his myths became closely associated with the theme of Hellenism vs Barbarism in general, and in particular served to emphasize the role of the Athenian democracy in defeating the Persians at Marathon and Salamis. This association was strengthened by the tragedians. In Sophokles (Oedipus at Colonus) and Euripides (Supplicants) we find Theseus portrayed as a very gentile, level-headed spokesperson of the democracy. This itself is a complicated matter, because Theseus was simultaneously celebrated as a competent monarch in the democratic age. John Davie has a pretty good summary of what I've said here, and more on Theseus as archetypal King (Greece and Rome 29.1(1982):25-34.
edit: spelled Hellenism wrong somehow