So I could be mistaken here, but it sounds like more understanding is needed on the differences between a proper and posterior and a likelihood.
Your posterior distribution can ‘change shape’ from your prior due to your data.
But there’s likelihood is something different. This is not something that changes, it is a statement about how your data are distributed. So choice of the likelihood is often very important. You need to consider whether your data are continuous or discrete and what the support is ie. Positive only, bounded etc
Let me know if I’ve misdiagnosed the issue here but hopefully that’s useful