How can I remove commas when adding tags?

Commas aren’t stored in the actual tag, they’re injected when tags are rendered. Whatever your tag-removal solution will be, it’ll happen via your theme files (or a plugin), and not when you input tags in the editor.

Here’s a quick shortcode solution for specific usage:

Place in functions.php:

add_shortcode( 'tags_no_comma_shortcode', 'get_tags_no_comma' );

function get_tags_no_comma() {
  echo the_tags(' ',' ');
}

Then use [tags_no_comma_shortcode] in your post or template file.

After this you may want to use CSS to give some styling for each item, ie ‘coloured pill shape’ (which is what a lot of people desire when removing commas).