Who has decided who can perform the Hajj? How long have e.g. Indonesian muslims been allowed to Kaaba. Has the access to Kaaba been subject to political pressures and how?
Whoever controls Makkah. So, historically:
Rashidun caliphate --> Umayyads --> Abdullah ibn Zubayr --> Umayyads --> Abbassids ---> Mamluks ---> Ottomans ---> Sharifs (technically been in charge since the time of the Abbassids but it was only post WWI that they were considered independent. And this was for a year) ---> Saudis