The word "tinge" literally refers to color mixing. If we take a pail of white paint and we mix in a small amount of red paint, the paint now has a red tinge. Speaking figuratively, it is common to use colors as a metaphor for political opinions. In the United States we speak of "the political spectrum" and refer to "red states" (Republican) and "blue states" (Democratic). In the context of politics, a "tinge" would mean a slight leaning or tendency toward some political opinion. From a Google search, I found that your passage is talking about the Primrose League. It was founded in 1883, and was important into the 1900s. "Habitations" are their name for their local clubs and meetings. The passage says that the group was politically conservative. However, it says that most of the time, in small local meetings, they more or less hid those views. They didn't talk much about politics. They appeared to be just a social group that organized teas, dances, concerts, and suppers. But in their big national meetings, "the political tinge of the group became clearer." In the national meetings, it was easier to see that they were a conservative political organization. In your passage, "tinge" is probably being used because the Primrose League wasn't literally part of the Conservative Party. In one metaphor, it had strong conservative "leanings." In another, it had a conservative "tinge." To carry the color metaphor farther, when they got together in these large meetings, they showed their true colors. In the United States in the 1950s--before the color associations changed!--the color "red" was connected with Communism. Communists were "red." People who were not Communists, but who were sympathetic to Communism were called "pink." The color pink is white with a red tinge.

Tinge is a slight color. example: The white flowers had a pink tinge. Tinged used in this context means that the political beliefs of the group could be understood when they were together.