first of all, i'd say that the term "taking advantage of" is incredibly loaded/biased because it suggests that the rioter and looter's mindset is purely self-interested and does not have a real or--even worse--"legitimate" political focus.

One of the best overviews of rioting in American history--paul gilje's "rioting in america"--rejects this view and instead identifies "ghetto riots" as a distinct form of rioting that really only emerges on a large scale after WW2 and is primarily done by oppressed groups lashing out at a social/economic/political "SYSTEM"--not individuals--that they feel severely oppresses them. To compare this type of rioting with other types is a mistake, gilje argues, because it ignores significant elements of historical context. The biggest element is the feeling of alienation between ethnic groups, racial groups, business leaders, and various levels of government that began significantly increasing after 1800 after non-british immigration increase and there were more free blacks. These groups relied on old forms of social ties to unite their communities, so outsiders frequently were viewed as threats. The more alienated people feel from the other groups or a "system", they more likely they are to lash out at it violently. This is why the 19th c had so much violent rioting (much more so than the 20th and 21st c).

Looting, furthermore, is especially contemporary as it reflects a consumer-based society where relative levels of abundance of possessions become more disproportionate. Consumables become the main object of desire in a consumer-based society, and the poor are frustrated because of their relative deprivation. Also, the police and military are much better organized, equipped, and deadlier now than they were before 1900, so it is more reasonable, if you are going to riot against the "system", to try to tear down the "gates" of the "system" (ie the doors to retailers).

In the 18th c, there wasn't as much A) alienation between the rioters and the "victims", and B) difference between amounts of levels of possessions--in fact, many of the numerous rioters during the revolutionary period were wealthier than the people they rioted against. Plus, as I said, the police and military couldn't control the rioters as easily.

There were many riots in the revolutionary period. Actually, there were so many riots between 1765 and the 1790s, Gilje labels that time as an "epidemic" in rioting. During the war and immediately after, rioting often targeted tories and the draft. Tories got their houses and business torn down and their bodies tarred and feathered.

those are just some thoughts...

I don't have any data before 1780, but between 1780 and 1783 there were numerous riots protesting paper money and targeting loyalists. In 1781, working poor roamed around Philadelphia trying to prevent anyone from using paper money. In May 1781, sailors and militiamen paraded through the streets of Philadelphia with a dog that they had tarred and covered in Continentals. A few days later, sailors who were armed with clubs, with the assistance of some carpenters refused to work unless paid in hard money.

Loyalists were also targeted as the British evacuated. On July 11, 1783 in Charleston, Tories and rebels 'battled in the streets' and Tories were tarred and feathered and threatened with 'worse violence' throughout the year. As the British evacuated NYC in November 1783, Whigs went around pulling down tavern signs that were owned by Tories. A group of wives also threatened to hang a British officer who had been in charge of one of the British prison ships and it was only the intervention of George Washington that stopped this.

Rural tax protests also started in 1781 - 1782 in western MA.

The research on political instability in the United States by Paul Gilje that was compiled in a spreadsheet by Peter Turchin is quite interesting.