WTF & ITF are more styles than Associations but correctly they're Federations, they are two different systems of taekwondo named after their respective organizations, the ITF and the WTF (Kukkiwon). The ITF was founded in 1966 by General Choi Hong Hi. I am with the TAGB also which studies the ITF style (style) of Taekwondo, ITA if you mean Irish Taekwondo Association is also a affiliated to the ITF system or if ITA is Imperial Taekwondo Association then it is also ITF style (system), if its not one of these then ask your instructor.
I don't think there is that much of a problem in competing for Olympic squad. You want it - join a local WTF style school pay the licence and up you go. Here in my country there are even several school with multiple affiliation, sending their students to Taekwondo International competitions and WTF competitions as they want to have support as an Olympic sport. There were several ITFers wanting to compete - they had their grades confirmed, took part in the national championships. 1st Dan is enough to take part, you may even have your ITF Dan confirmed, no need to climb up the ranks from white belt up. Honestly, if you want to be a top Olympic Taekwondo player, it's not enough to do say ITF style and add an occasional WTF sparring class here and there. It's a different story and even if you may do well on a regional or national scene, it doesn't have to be enough for big international events. Some ITF World Championships medalists did well in Polish Championships but took a hammering on the European Championships. If your goal is the participation in the Olympics, do the Olympic style sparring 100 %.
