Idk if this is something this sub can answer, but why is the IRA always painted in a sympathetic light on tv?

Weren't they blowing up cars and killing ppl based on religion?

No. Catholic/Protestant is a convenient dividing line, but it was really Nationalist/Republican/Loyalist/Unionist. I would also observe that I presume you are referring to the Provisional IRA. We had a bit of a joke going that we in Ireland were safe from foreign invasions: We have the Irish Army, the Irish Republican Army, the Continuity Irish Republican Army, the Original Irish Republican Army, the Provisional Irish Republican Army, the Real Irish Republican Army, and the Sisters of Mary. (All but the first and last are actual terror groups. Those who went to catholic school and got taught by nuns may wish to include the last as well)

I'm a little surprised I can't find an immediate answer on askhistorians as to "what happened in the 1970s", but the bottom line is that the violence really got going not so much over geography and territory, but lack of equal treatment between the people in the generally protestant areas (who happened to be generally unionist/loyalist) and those of the generally catholic areas (who generally leaned nationalist/republican). Yes, the whole six-counties/united Ireland thing had been going on in the background ever since the Civil War officially ended the squabble, but it was the demand for equal treatment by the Northern Ireland Civil Rights Association, who saw the civil rights thing generally be successful in the US and decided to give it a go, which was the catalyst for the Troubles. The Northern Irish Government was far from even-handed in its treatment of the protestors, and the paramilitary groups such as the PIRA became the only group capable of offering armed resistance and security in the Catholic areas.

When London decided to send in the British Army, they were initially viewed as neutrals, and welcomed by the Catholics. A strange response if you only consider the British forces as imperialist occupiers. The problem was that being soldiers, they followed their instructions, and their instructions were to follow orders from Stormont, the Northern Irish government (London wasn't really paying much attention to the fine details, something PM Wilson was later to regret). The other problem was that being good soldiers, they enacted policies as best they could. Their operation on the Falls Road was an excellent example of initiative and military competence, unearthing weapons caches and personnel, only to see it turn into an utter disaster by their rigid enforcement and dealing with a tactical problem. They won the battle, but started the war, if you get my drift. The Falls Road Curfew became the point at which the British Forces really started to be seen as the enemy.

From there, folks started to get away from the Civil Rights angle, and it became a matter of "If we're going to be fighting these guys anyway, let's go back to the original goal of the 32 counties. And we won't need to demand civil rights off the British because we won't have any say any more!"

There is much more to be said on this sort of thing. I'll tag /u/ChuckRagansBeard in the hopes he'll fill in a bit more.

As far as the level of 'sympathy'... well, I guess it depends on who you ask. There is a perception in Ireland that the PIRA et al were seen far more sympathetically in the US than in Ireland. I remember walking into a bar in San Francisco named "Ireland's 32." I saw the decor on the wall, glorifying the PIRA and its attacks on soldiers, and walked out again. I cannot for the life of me recall ever seeing such a bar in Ireland. Much of the PIRA's funding came from the US. So, yes, I would not be surprised to see occasional sympathetic portrayal in the US.