Okay, two things. One, trade restrictions make the world "larger" by increasing the cost of moving goods and services. Higher cost, less volume. We're less likely to sample the fruits of other parts of the world. Similarly, higher oil prices, transport costs, whatever, have the same effect.
Thus, if oil was at $30 or whatever, would we see that much more protectionism? It seems that many people have a preferred world-size in that they want some trade, but not totally free trade - or just derive a certain amount of utility from inertia. If so, the increase in transport costs would lead to an increase in calls for freer trade.
Certainly, Obama's protectionist rhetoric has cooled as oil heated up, and McCain was in Ottawa the other day to extol the benefits of NAFTA with oil at record highs. If we had some sort of "index of global protectionist sentiment", I'd like to bet that it would exhibit a negative correlation with a one-year lagged time series of shipping costs (for which we could use the Baltic Dry Index, no less!)