This is a great question. One I'm sure other players might have from time to time as well.
Firstly, all the tribes/clans mentioned being "open" on the website - are open for play.
However, most of them also have a limit on how many players can be active and alive in those tribes/clans at any given time.
Your best bet would be to put in a request, choosing the appropriate tribe/clan from the drop-down menu in the Request Tool, and ask:
a) Hey, I'd like to play a role in this tribe, I understand it is open. If there are slots available, could you let me know what types are available.
b) Could I have access to clan documentation.
Once you have a response, you can submit your concept for approval and take it from there.
If you're without a PC and would like an immediate response, please feel free to say so in your request. Staff does try to expedite those.
So, to summarize, even if certain clans/tribes might be open to play, they might not have a slot currently available. Or, they might have available slots, but possibly not for the concept you might want to pick (for example a particular type of magicker).
It's not possible to update the website so dynamically, so a Request is your fastest bet here.
Usually those kinds of requests are replied quite swiftly, but sometimes there might be delays, due to RL, so take that into account.