They can flip-flop on any given issue, and it's of no consequence
This is extremely easy to verify for yourself -- reset the context, vary your prompts, and hint at the answers you want.
They will give you contradictory opinions, because there are contradictory opinions in the training set
---
And actually this is useful, because a prompt I like is "argue AGAINST this hypothesis I have"
But I think most people don't prompt LLMs this way -- it is easy to fall into the trap of asking it leading questions, and it will confirm whatever bias you had