So, the question is whether contemporaneous use within a single community suggests that they were viewed as the same or distinct. Either is possible. If they were considered "font" variants, then you might expect to see different documents using one or the other, or see different elements within a single document using one or the other. But if you see documents containing equivalent content repeated in each, then that might well suggest they were viewed as distinct.
The examples brought by Dean Snyder from ancient Judah seem to be either different documents using one or the other (for a loose definition of "documents") or different elements (the Tetragrammaton, scribal redactions) within a single document using one or the other.
The examples from modern coins vary. The 10-shekel at http://www.bankisrael.gov.il/catal/c41.gif has equivalent content repeated in each, but the 1 shekel at http://www.bankisrael.gov.il/catal/c39.gif does not.However, I discovered when using a shekel coin to do my own survey of the legibility of PH in modern Israel that most people simply assume that it does: almost everyone who thought that the PH was writing at all thought that it said "Shekel".
So if Peter's premise is correct, and it seems reasonable to me, the limited evidence seems to suggest that Palaeo-Hebrew and Square Hebrew were viewed as font variants by Hebrew speakers 2,000 years ago, and as separate scripts by Hebrew speakers today.
