Second, the IRA had military and police targets to hit, so they hit them, the UDA/UVF had only civilian targets (because the IRA was hard to find) so they hit the Catholic community. That is a difference of circumstance, not of morality. But the raw data could well be used to support the idea that the IRA were a legitimate army (like the British Army) while the Loyalist paramilitaries were a bunch of thugs (i do not subscribe to this natrative).
I still condemn the use of violence in places like Iraq, when the British army was sent in; so even if the IRA was acting like a real army, i would condemn them.
That said, the British Army was not originally sent in to stop them. It is important to note, when the Army went in (and i still think it is a terrible idea to send in an army to do policing - but maybe it was the best bad idea the government in Westminster had at the time). They stood between the RUC (police) and the Free Derry protesters (Civil rights groups who started out as non-sectarian and peaceful).
This is a tacit admission that Westminster didn't think the RUC was doing a good job - but unfortunately didn't de-escalte the situation. At the time the IRA didn't have much support, but the escalation lead to the bloddiest day of the troubles, which the data shows as 1972-1976.
Anyway, there has been claims that the RUC supported Loyalist terrorists by giving them weapons and otherwise. And it is likely that some members of the British Army (as you put it a few had eggs) later joined this systemic discrimination against the Catholics (the IRA was targetting them after all).
So you can see that (if not exactly how) the situation moved from a peaceful non-sectarian civil rights movement (asking for things like "One Man, One Vote", and to address a housing issue) into a sectarian conflict where many Carholic Protesters (probably like Martin MacGuinness) moved from peaceful protest to supporting the IRA. (Of course before the cease-fire and peace process, Sinn Fein, the IRA's political party, did not have the support of even a majority of Catholics, because on both sides a majority did not support violence).
Still the constant discrimination, the state security apparatus supporting loyalist terrorists, and the RUC's failed policing, are the root causes that ignited this conflict. So i can equally see many IRA supporters saying, 'well the brits were killing us, so of course i supported the IRA fighting back'.
Like you i sympathise with the members of the British Army sent in to stand in the way. They were just following orders. They were not ordered to shoot anyone, but unfortunately that is what they were trained to do. And it was almost inevitable that, once they were sent in, the situation would escalate.
I would again cite poor governance from afar*; and the current power-sharing agreement is a far better situation. (Even if it means making peace with Former terrorists like Martin MacGuinness, and Sinn Fein or the Loyalist opposites).
*Devolution and Independence to avoid the worst effects of the British Empire. The worst being famine in India in the 1860s, which ou should really read about.