The anarchists, qua bombings, played a potent role in 19th, and early
20th century politics, but not a good one.
Politically, anarchists are really quite different from the
socialist/communist tradition:
- Anarchists: reject the state
- Socialists/communists: reject capitalism
Naturally there could be overlap, and indeed there is a well-known
tradition of anarcho-communism [1] which was especially potent in the
Spanish Revolution of 1936 (note that there were bitter fights between
anarchists and the Stalinists), but at the same time, it's difficult
to reconcile the philo-capitalism of the libertarian wing of anarchism
with the socialist tradition. Likewise, it's difficult to reconcile
the philo-stateism of the socialist tradition with anarchism.
As to "mature": as a first approximation, I'd say, having a written, elaborate and communicable theory behind one's political actions, one that has survived multiple round of (friendly) critique. A mature political position includes reflection on the nature of political power, the shape of politial organisation, and political activism, and clear end goals with reasons why the desired end-goals are likely to come about. A mature political position also contains an understanding of other political positions, including those of one's political adversaries.
An prime example of a mature political position is Marx.
As an example of political immaturity, I'd point to myself when I was 19. I was nothing but an angry, raging young person, who railed against "the system", wanted to "stick it to The Man" and save the world. But I would not have been able to explain why, in way that I would have found plausible.
[1] https://en.wikipedia.org/wiki/Anarcho-communism