>But surely mentioning the motivation for their crime is relevant to the case and should be admitted in court.

It's their defence. So they would be saying that the fact that they did something because of climate change should have some effect on their guilt or sentencing.

Most decisions made in court have an effect on subsequent cases, so accepting it might set a precedent for these kinds of ideological beliefs to be accepted in court.

It's fairly obvious why fighting climate change isn't allowed in someone's defence.