Great question! I'm a fan of the series so it's fun to talk about it.

Simply, the British support for sending soldiers to the American colonies to put down this insurrection was not a universally supported position. There were members of all classes that did not support the war in the colonies in Britain, however the merchant class was the most vocal (mostly because they were the ones most directly impacted in the prelude and during the war itself). As award winning historian Alan Taylor discusses in his book American Revolutions multiple senior officers in the British Army who served in the American campaign personally opposed the war, but many felt they would still serve to honor his country and bring personal glory to himself and his family.

Perhaps most famous of all to serve but still voiced opposition is Gen. William Howe, who had publicly voiced opposition to the legislation that was enacted to punish the 13 colonies, most notably Massachusetts in the years before the war ( David Hackett Fischer. Washington's Crossing. New Oxford University Press. 2004. pp 70-71). In 1774, he even publicly stated he would not go into active duty abroad to fight against colonists saying he thought that the the Americas could not be conquered, although he ended up betraying this statement the following year. However, part of his public declarations appear, at least in part, to be insincere, since by early 1775 Howe was telling some members of the Ministry in private, that he would be willing to serve under Gen. Thomas Gage in the Americas. When King George III did call him up, he eagerly agreed in private yet publicly said he did so because: "My going to America was not of my seeking. I was ordered, and could not refuse, without incurring the odious name of backwardness to serve my country in distress."

Ultimately, many of these officers still decided to serve (some did not have an entirely voluntary choice due to familial obligations). If Poldark had been a real person rather than a work of fiction, it would not have been out of the ordinary for him to oppose it, especially since it was an extremely unpopular war by 1783 (which is when the show begins if I remember correctly).

Edit: added more information about Howe.