It would be like saying why isnt GG a part of the Galactic Republic. The Old Republic is an organisation not a time period. The sith (the enemies of the republic) are most certainly not part of this.
Now as for why characters like Visas Marr and HK arent a part of it. Well I reckon its because the Old Republic also means in this case, synergy with Carth, JKR and the rest of the group. So Visas Marr didnt travel at this time so no synergy.
HK is an old toon whos getting a rework, he will prob get the Old Republic tag.
Even Fallen Bastilla would know how to operate with either side as they have worked together.
Im not saying its perfect and obviously the game has to justify certain interactions, but there are clearly bonds between the characters to justify