Learn English – A word for showing a bit of anger that you are not satisfied with what is offered

Smarmy is a possibility; it means "Falsely earnest, smug, or ingratiating." Also weaselly, in sense "A devious or sneaky person or animal", may apply. An uncommon word that might be relevant is fugacious, "Fleeting, fading quickly, transient", if you expect support to just forget the issue immediately.

More along the line of "empty promise" are words as found in a clique of illusory synonyms: chimerical, fancied, fanciful, fantastic, fictitious, illusory, imaginary, unreal, and similarly for fictive and perhaps for tenuous, "thin in substance or consistency".

Empty promises in the sense of "say what they want to hear" often are called blandishments, which is defined as "flattering speech or actions designed to persuade or influence."

Empty promises may also be evasions, lies, sophistry. Among the senses of the latter are "an argument that seems plausible, but is fallacious or misleading, especially one devised deliberately to be so"; "the art of using deceptive speech or writing"; and "cunning or trickery".

There are a lot of words that mean "having an extremely strong opinion." Here are some good ones.

Ardent

Passionate

Zealous

Fervent

Vehement

Also, Partisan. Someone who is so strongly in favor of a particular cause of another is called partisan. This is generally used in politics to describe members of political parties who only act in their party's best interests.

For the second question, a word that describes a situation where one can only believe one way or the other:

Controversial

Polarizing