They have a problem, or in brief disapprove, of the world in some way. However, this world cares nothing for such understanding of it, and instead just subjects them to 'shame and punishment' without any pause for thought, which they see as a distraction from their aim of understanding it, wherever that may lead. However, their considerations cannot be idle, for a thought, if honest, is also an intention, or what we think directs our conduct - unless perhaps we are drunk -, being human, so hence 'intentions are valuable as deeds.'

The harmony between a wound making them 'bleed' and people figuring that 'what's in their hearts is right' is a bit bloodthirsty, but may be inadvertent.

The chorus is basically sarcastic - obviously they're being disagreeable for most of the song - and refers to the situation of the 'world' at the time being such that people are encouraged to be assured that whatever their instincts or feelings on a question, they are 'right,' or in brief people will simply act out or to undermine or marginalise them because of their own interests or feelings, rather than considering anything universal or true. It is hence described as 'pathetic,' or a relativistic submission to the feelings of anyone. This merely led to a lot of people who could merely act according to their emotions and instincts, and not any particular universal considerations reaching beyond this, which they had problems with. This hence also made them passive, or they could not judge foreign inspirations or persuasions negatively, in a consistent manner.

This song brings to mind another song, "Best For You," though "In Their Hearts" is more from the "outside looking in" than being judged by others as is the case for Best For You. Nonetheless, those judging in Best Fir You obviously feel "what's in their heart is right." In both songs their seems to be a sense of "shame" that drives us to behave, and similarly a question as to whether there is an ideal to strive for when in reality life is "senseless," as is the idea of an ideal right and wrong. If, by chance, "shame and punishment" is a reference to Foucault's "Crime and Punishment" and both songs point to a similar post structuralist or nihilist worldview of a "senseless" life bordered with people's "hearts" and views of what's "best" and how to push people into "understanding" how to behave/believe in a culture (or sense of rights and wrongs) I can't say. However, to me this view makes sense.