How can I make front page to display custom taxonomy page?

I agree with @KrzysiekDróżdż While you should probably be able to do this it might be unnecessary work.

However, this works with I test it, just change the category/term name and the template name (the part in get_template_part), and maybe the is_main_query() && $qry->is_home() conditional if you need to:

function pregp_home_cat_wpse_104619($qry) {
  if (is_main_query() && $qry->is_home()) {
    $qry->set('category_name','aciform');
    $qry->set('ignore_sticky_posts',true);
    add_action('template_redirect','tr_home_cat_wpse_104619');
  }
}
add_action('pre_get_posts','pregp_home_cat_wpse_104619');

function tr_home_cat_wpse_104619() {
  get_template_part('category','aciform');
  exit;
}

I have never tried to do this in production, so “when I test it” means that I’ve spent about 10 minutes and don’t see any obvious problems. I make no promises.

Barely tested. Possibly buggy. Caveat emptor. No refunds.