>This doesn't seem very rational. If your beliefs are in conflict and you're content to not resolve that, then pretty much by definition you're accepting a logical inconsistency.
This is just my perspective, but very few beliefs or values map to the whole of reality...they tend to bind to certain aspects of it with a variable priority along the spectrum of that particular dimension, wither its personal agency, the color red, public health, spiders, etc.
However, reality rarely provides us with the ability take a position purely on one factor...nearly every context in which a decision is required operates at the nexus of an uncountable number of these dimensions. Some you can feel swelling to the fore as their slope in your mental 'values' model increases, others stay dormant because you don't see how they apply. This is how most of my decisions that might look outwardly 'inconsistent' arise, there are confounding factors that dominate the topology and steer me in a different direction.