Studies suggest that genes play a significant role, and obviously there's an environmental component (ie your upbringing, for which your parents are very important but many other factors play a role, too). Hence you generally take on the ideology around you, even if that may slowly shift between generations (but it seems that people also simply have a different mindset at 20 vs at 40, so when you ask them at 20, they're very different from their parents, but that often changes when they are in similar circumstances as their parents).

Of course, some people do change their ideology later in life (which I don't think is the right term, because they don't actively change it, it's more that they change and their ideology is part of them), but that's not common, and overall it's remarkably stable.