Use the noun hardliner to describe a politician who sticks stubbornly to a particular position or policy. It's most common to talk about a conservative hardliner.
While most hardliners have fairly extreme conservative opinions, you can use the word whenever you talk about a politician who is unwavering in her devotion to a specific idea. Most successful politicians find it useful to compromise, at least from time to time, but hardliners are known for being unwilling to change opinions or accommodate other viewpoints. The word hardliner was first used in 1963, from hard-line, an adjective used in the 1950's to describe Soviet communism.