The 'inheritance of acquired characteristics' is something which effectively underpins any view of humankind that sees consciousness as 'evolving'. "Look at the wonderful technology we now have, all the social reform, etc, etc" - human consciousness must be evolving! In other words, the acquired achievements of one age are inherited by the next.
This is a debate which raged in biology (it takes me back to Bateson, so comfortable territory!), concerning the development of Giraffes' necks and Elephants' trunks. Because one giraffe had to stretch, its descendants grew longer necks.
It is merely an idea, but a powerful one (which has for some time been discredited by the scientific community). It still exists in various forms - particularly in Dawkin's work.
What are it's political implications? The real problem for me is that it suggests that one idea is more enlightened than another, and that this idea will be inherited by future generations. Whose idea? Why theirs? It's an open invitation to manipulative people to expoit and abuse positions of power.
All-in-all, these political problems are a testament to the causal powers of ideas, which in many cases must be guarded against. The defenders are always human conscience and decency.
The social efficacy of some ideas is clearly better than others. What that means is that some distinctions are more effective than others at any particular point in history. At this point in history, Lamarck serves us poorly. Luhmann might be more interesting...
This improvisation is set to a diagram I did with Jim on the relationship between Shiva, Vishnu and Brahman and the VSM.