As a Brit, but not a teacher, I would read the 1st sentence as referring to potential future actions, but the 2nd sentence as being time independent.
If a person were to be "accused" of a particular action either in the past, or considering it in the future, then a supporter might say that it couldn't possibly be true as: 'He would never do anything that goes against his conscience.' (i.e. either in the past or future).
As the feelings of native speakers move one way or the other, we move one way or the other with our word choice. When we feel that we are speaking about an issue that is completely hypothetical we move to the right and we use hypothetical language, past tense and historical past tense FORMS.
When we feel that the situation is a mix of hypothetical and more reality we mix conditionals.
Note the use of the underlined modals, above. In this, I'm sitting squarely in the middle of the scale and I can use any of the four modals. Certain situations just happen to fall on certain areas of the scale.