How open and inviting a club should be is a challenging question. I don't know of a club in my area that doesn't struggle with attracting new pilots and converting them into dues-paying members. Enforcement of a strict "no guests" policy and a lack of open house events where non-members are welcome almost guarantees your membership will decline. Be too welcoming, and pilots will hang out and fly at your field year after year without ever contributing to its maintenance and upkeep.
In order to get people to come to your field and fly, you have to get people to come to your field and fly. The obviousness of that statement is actually lost on some flying clubs. If folks come out to a flying field, and the members are welcoming and people are flying and having a good time, new people will want to join. If members aren't welcoming to new visitors, your club may be sunk before you ever get a chance to talk to a new prospective member.
Some of the members at my primary flying club don't want new members. They've belonged for decades and put in the time, effort, and money needed to maintain the field. They want to hang out with their buddies, fly in peace, and not be bothered by a bunch of new people taking up the good parking spaces and crowding the flight line. If a prospective new member talks to one of these guys, they'll go find a new hobby rather than trying to learn to fly at your club. Why put up with that kind of attitude when they could go geocaching or learn to blow glass instead?
The AMA grows when its member clubs grow. I don't know anybody who started out wanting to join the AMA, and then decided to join a local club and learn to fly because it was expected for AMA membership. The way to grow the AMA is to grow your local flying club. Welcome new visitors, thank a spectator for coming out to watch and offer them a cold soda, help beginning pilots and encourage their growth, present the sport of model aviation to a wide audience in a fun and positive manner. If your club is having a good time, people will want to join to get in on the fun. When your club grows, the AMA grows.