How to avoid filling up an array each time I run a WP_query?

The obvious first step would be to use get_col instead of get_result. You will get an array returned straightaway so you could skip your foreach and go straight to:

$args = array(
  'author__in'     => $following_users_ids,
  'posts_per_page' => 12,
  'paged'          => $paged,
);

Behind the scenes, get_col does much what you are doing but you are not going through the more complex get_results function before doing it.

With thousands of users, I am not sure that that particular operation is going to be holdup that you think. That is, I’d suspect that maybe the delay is elsewhere, at least a significant part of the delay.

I’d suggest that:

1. You make sure you table is indexed correctly
2. And you cache the results— possibly cache both the IDs and the
   post results