To me, the infinitive forms a unit with the verb of liking, so in (b) and (d) it is clear that the speaker likes or hates to do those things him/herself.
The gerund preceded by an adjective in (a) and (c) functions as a noun and creates a sense of detachment: the speaker likes or hates those activities, regardless of who carries them out.
However, with other gerunds the speaker's involvement in the action may become more evident, as in:
e. I like open water swimming.
f. I hate open water swimming.
When the gerund reflects the result of an action rather than the action itself, the sense of detachment reappears, as in:
g. I like/hate Peruvian cooking ("cuisine" is more usual but "cooking" is also possible).