Historically, there hasn't been a major political party in the United States that has taken an official stance opposing the inclusion of the word "God" in the Pledge of Allegiance.
However, certain individuals and groups, often associated with secular or atheist organizations, have raised legal challenges to the Pledge based on the Establishment Clause of the First Amendment, which prohibits government endorsement of religion. These challenges argue that including "under God" violates the separation of church and state.
It is important to distinguish between the views of specific individuals or groups and the official platform of a major political party.