I understand that in a hardfork (e.g. the actual Bitcoin vs. Bitcoin Cash/Gold) the blockchains would diverge because the miners and clients have different rules to accept a valid block. It makes sense to me how you could get two or more divergent databases in this way, theoretically.
What's less clear to me is how the actual network joins itself together in practice. Are full nodes on one chain constantly bombarded by the blocks of the other? What keeps a spend [of pre-fork holdings] on one chain from accidentally — or for that matter intentionally! — propagating to the other?