Okay, this is going to be a pretty sprawling answer because this is a sprawling question. Not a knock on you whatsoever: it's a fascinating issue to cover.

I need to start by saying that I too have seen people comparing current American political strife to the Troubles. I will say absolutely no more about it - because the 20 year rule exists for a very good reason - but need to make it clear that it's an incredibly odd viewpoint, given what the Troubles were and why they happened/how they were conducted.

So: the average person. That phrase is doing a ton of heavy lifting in your query, and it's important to point out a couple of facts about Northern Ireland and the Troubles. In the early 1990s, as the Troubles were nearing their "end", the population of NI was around 1.6 million. The death toll - according to David McKittrick's truly excellent work "Lost Lives" and the CAIN online resource - was 3,532, with around 48,000 injuries of varying severities. That is an absolutely staggering number given the proportional representation. And you are also correct: the majority of these incidents happened in Belfast (the largest NI city) and Derry (the second largest and, for my own sake, please forgive me for not typing out Derry/Londonderry every time it comes up). However. the conception that more rural areas were unaffected is entirely untrue. Northern Ireland is made up of six counties: one of the rural areas, County Armagh, was known as "Bandit Country" during the 1980s, because the PIRA was heavily active near the southern border. It was an incredibly dangerous place to be for British security forces: the Armagh Brigade of the PIRA shot down British helicopters and killed dozens of RUC (Northern Irish police forces, at the time) during the 1970s and 1980s.

That does not directly answer your question, but I wanted to make it very clear that Troubles violence was not, in any way, strictly an urban issue. More to the point, the PIRA and their adversary paramilitary forces like the UVF often conducted training, weapons storage, and recruitment in the more rural counties, especially those along the border. So what impacts did this have on daily life for the "Average Person"? Im assuming here that the average person is not affiliated (outwardly) with any of the paramilitaries and is not a member of the security forces. Even that assumption leaves us flying a bit blind, as the experience is going to differ WILDLY based on whether you are a Catholic or a Protestant, political or apolitical, what country/town you live in. Your gender, of course, as well.

What all involved would have noticed were checkpoints. Military checkpoints that searched cars and persons; even fake checkpoints erected by the paramilitaries for their own purposes. If you lived close to Derry, and needed to go over the border to the west into the Republic of Ireland for farming supplies, you might be driving through the same checkpoint half a dozen times a day. Security alerts were another. Real bombs, fake bombs, bomb threats: these alerts were issued all over the six counties, not just in Belfast and Derry. The CAIN resource (which is free and I cannot recommend it enough) estimates around 10,000 bombs were used during the three decade conflict. Again, that is absolutely staggering to conceive of. Your road to work might be shut down. Your favorite chippy might be behind a police barricade. These are the daily occurrences most central to your question, and would have affected both sides to a degree: that being said, as the RUC was a predominantly Protestant run force, these security measures were often over-deployed in Catholic centric areas.

A bit of personal editorializing: I joined an Irish Falconry group recently. Doing some digging into the history of falconry in Northern Ireland, it's absolutely fascinating to read about the period from 1968 to 1998. Your average person - well, as average as a falconer can be - walking around in the brush of County Tyrone could get the RUC called on them pretty quick. There's a level of suspicion that goes along with this type of thing, especially in a country where everyone seems to know everyone local. Many commentators and journalists from outside NI have commented that, during their time covering the Troubles, it was astonishing how locals seemed to know what "side" everyone they came across was on. The cultural influence that underscored the sectarian nature of the Troubles also affected people who were otherwise unaffiliated. The Orange marches on the Protestant side; the marches celebrating the Easter Rising on the Nationalist side; the music you listened to, the pubs you frequented. All of these were inherently political choices. It was something which permeated so many aspects of common life.

I want to recommend whole-heartedly a short story/novella collection by Irish writer Colum McCann called "Everything in the Country Must". It's not a history text, but it is an excellent work of fiction that gives a really tragic insight into people dealing with these issues. For historical context, I recommend McKittrick's "Lost Lives" and his general text "Making Sense of the Troubles". For individual memoirs and insights into life at the time, Eamonn McCann's "War and an Irish Town" is excellent: McCann was not a member of the paramilitaries, but was a socialist activist and student revolutionary.