Learn English – Meaning of “push in direction of”

To understand your passage

On the contrary, coherence work of the moral kind pushes in the direction of less influence by those unthinking processes and the presumptions they spawn—all variations on "me and my kind are worth more than you and your kind".

One needs to take note of the preceding passage

The reasons we are prepared to give to ourselves and one another in accounting for our behavior make no mention of the machinations of the selfish gene.

the coherence work alluded to is

the reasons we are prepared to give to ourselves ... for our behavior

is the explanations that humans come up with to understand their existence.

The unthinking processes alluded to are gene survival at any cost.

Greedy genes will choose themselves over others

me and my kind are worth more than you and your kind

in an unspoken process (survival) and will continue on regardless of any reasons humans come up with for human existence.

The entire article talks about existence and how philosophy as a school of thought is used to explain existence and the necessity for such explanations and the dichotomy between what is explained and what actually happens