A lot of them don’t seem to care about what’s happening in this country

That's good advice, but if only 1 in 6 non-voters will come to the polls if their church leader says they should, it's not very encouraging advice. It would be more encouraging advice if the fraction was 1 in 5 or 1 in 4 or 1 in 3.

Eph 6:12 - For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places.

And isn't one of our 'weapons' the ability to vote against such people and establishments?

Yes, it's a weapon, but the effectiveness of said weapon depends on what its target is. You don't bring a knife to a gunfight and expect to come out alive.