Ignoring my concern over your lack of grammatical accurate syntax, I think you’re asking why Americans don’t see hypocrisy in financially supporting the Provisional IRA in the ‘70s and ‘80s, yet are against other forms of terrorism.
I would ask, as sndfreQ said, for the evidence that supports the claim that “so many” openly supported the Provisional IRA. If you are talking about political and financial support for Sinn Fein, you are conflating the two, which is very dangerous when trying to untangle the mess in Northern Ireland.
Sinn Fein, while once being the political arm of the original IRA, had few legitimate ties to the Provisional IRA that was reborn in the 70s. In fact, the Provisional IRA had no real ties to the original IRA save for the name. The link that people make between the two is that Sinn Fein refused to reject violence as a tool towards independence. Whether they meant violence towards the state or the sort of indiscriminate violence that the Provisional IRA represented is up for debate.
Yes, Sinn Fein could sometimes influence the actions of the Provisional IRA, but the Provisional IRA remained completely autonomous. To a much different extent, it’s the similar to how, in the U.S., the Democratic Party can sometimes reign in ecoterrorists like the Animal Liberation Front or the Republican Party can sometimes reign in extreme white power groups. It doesn’t mean they are one and the same, just that they have limited ability to negotiate with them based on their political affiliation.
You also have to remember that a significant portion of the population of the United States wasn’t old enough to have an opinion about the Provisional IRA during the beginning of the Troubles. If you argue that the United States supported the Provisional IRA, you have to confront the fact that United States (as a state) is historically connected, but that the population of that state is much further removed from that historical context.
Personally, as an American of strong republican Irish descent, I continue to be conflicted by the Troubles. I do not support the Provisional IRA and I wish that Sinn Fein had more strongly denounced their tactics, but like Sinn Fein I feel that a people have the right to turn to violence when removing an occupying or colonizing force. However, I believe that the right only applies to violent acts directed towards the state, and that the right is forfeit if used against innocent civilians.