Is the first degree (bachelor's degree) of any importance for postdoctoral training?

Well, I'd guess you need to start somewhere. Some Unis offer masters as a first degree, but the first is usually a bachelors.

for postdocs, is the first degree of any importance?

It probably depends - if the post-doc is in a similar area to your PhD, then first degree probably not important. But if you developed skills in your first degree (that you might not have used during PhD) that are relevant to a Post-doc position, then that has to help?