Word for bigotry towards someone of political beliefs

Consider political zealotry, political activism, and political militancy

zealot: a person who has very strong feelings about something (such as religion or politics), and wants other people to have those feelings.

zealotry: excessive intolerance of opposing views

activism: a doctrine or practice that emphasizes direct vigorous action in support of or opposition to one side of a controversial issue

militancy: the active championing of a cause or belief

Still and all, zealotry seems what comes the closest to what you're looking for, as long as neither activism nor militancy connotes a deep-seated prejudice against political opponents.

A sectarian may fit your description:

one characterized by bigoted adherence to a factional viewpoint.

Sectarianism:

is bigotry, discrimination, or hatred arising from attaching importance to perceived differences between subdivisions within a group, such as between different denominations of a religion, class, regional or factions of a political movement.

The term chauvinism can cover it

smug irrational belief in the superiority of one's own race, party, sex, etc.

However, the term is not limited to views about political allegiances. To be explicit, you would have to preface it with a delimiting term, such as ideological chauvinism.

Also consider partisan

A strong supporter of a party, cause, or person.

This does not necessarily mean the adherent is blindly prejudiced against different points of view, but the usual connotation is one of a narrow-minded devotion to a cause.

A more colloquial term is drumbeater