But I see what you are saying: only ignore everything else if it is truly background information.
Ok, but there is a problem with application of that type of strategy. You cannot know if something really is irrelevant information that doesn't matter to solving the question unless you analyze how it relates to the answer choices before deciding it's safe to ignore.
Sometimes critical details that are key to seeing how/why the CR answers the question and/or why a trap answer doesn't are intentionally planted by the question writers in parts of the argument that may seem like irrelevant fluff at first when initially breaking it down to the core. This is especially true of the higher level difficulty LR questions that tend to be clustered in The Death Zone (roughly question #s 14-22 in each LR section). You'll tank big time on Qs in that range if you selectively decide to ignore parts of those arguments in your analysis of answer choices. It's pretty much guaranteed you'll get a bunch of the harder questions per section wrong if you adopt this as a universal strategy. It can save time on many easy to medium difficulty level questions, but will kill your accuracy on the harder ones that you need to get correct if you want to score above mid-high 150s.
There is no easy way to safely determine which questions are higher level difficulty ones where important details might be buried in seemingly irrelevant fluff versus ones that you can get away with ignoring entire parts of the text in the analysis and still get correct without trouble. The test writers abhor 'it always works this way' patterns that are susceptible to 'always just do this simple trick and it will work' fairly brainless non-analysis based strategies.
This type of strategy can help timing overall and work pretty well for the first 10 or so LR question per section but will intermittently/sporadically fail and cause you to get many wrong later in the section as the difficulty level increases. Since it also works well on at least one or two of the hard questions in the Death Zone that have annoying extraneous fluff and helps save a little time without missing those few questions, you get a false sense of confidence about the strategy since it helps you move faster through the entire zone of the hardest questions of the section without noticing that you easily fell for several trap answers designed to sucker people that ignored something that on first read sounded like irrelevant fluff.
Don't adopt this strategy unless your target score is no higher than mid to high 150s. If mid-high 150s max is an acceptable best possible outcome for you, this strategy can help to scrap together a few more points per LR section overall with limited practice.
Seriously, the test writers intentionally put a lot of effort into writing really attractive trap answers for higher difficulty questions that are specifically designed to sound super awesome and get you to jump at it right away if you completely disregard certain parts of the argument that were also intentionally written to sound fairly non-important during first read/breakdown of the argument so that people don't focus on it when debating the attractive answers. If you review LR question you've gotten wrong in the past that during review you determined were dumb mistakes because you forgot about a particular detail that makes the CR easy to understand in hindsight, you'll find many questions with good trap answers that are really appealing when you ignore seemingly unimportant background information.
In short, there is no reliable way to determine whether certain seemingly irrelevant on first read parts of the text are truly irrelevant to the logic behind the CR without actually analyzing it. Otherwise, you are just randomly picking parts to ignore based on gut instinct/feel before having analyzed and really broken down the reasoning of the argument. The LSAT loves to punish people that gravitate towards universal 'just do this simple trick' simplification strategies/shortcuts meant to avoid having to do some of the analysis in order to save time/speed up in the section.
A good way to make sure you don't accidentally ignore important buried details is to add a verification step in your analysis once you've read the answer choices the first time and narrowed it down to a few. Right after you've read the five choices the first time and identified which ones you think are contenders, reset and re-fresh your focus on the argument itself by re-reading it from top to bottom word for word to fully refresh your understanding of it and the details before
doing the analysis to make the final make or break it, get the point or not decision between the contenders.