I don't have a corpus so I'm basing this off the result of Google search: "une culture" is a singular noun, but it seems that "une culture qui ont" is 2 times more frequently seen than "une culture qui a". Why is that?
Sur tous les plans, vous contestez une civilisation, une culture qui ont mis des siècles à se faire.
Il y a des symboles sacrés universels ou propres à une culture qui font écho à l'humanité entière
This sounds like just a statistical anomaly.
In the first of your examples, the subject is "une civilisation, une culture" — which is plural because it's a civilisation and a culture that took centuries to build up.
In the second of your examples, the subject of "qui font écho" is "des symboles".
In the 1st sentence, the subjects are "civilisation et culture". In the 2nd, the subjects are "symboles". In each case, a plural verb is called for.
