Your question is slightly intimidating, but I will try my best.
First off, LIG is not a Utopia, if someone thinks or believes that, they are mistaken. LIG is a real proposal that has sufficient detail that it can be implemented reasonably. LIG has also only been conceived of being installed or implemented in a democratic society. Of course Dictatorships or Communistic states could implement it, however it may be odd since it is somewhat more democratic in design since the LIG company is owned by the people not the government or the ruler or dictator, which is kind of contrary to what control a communistic state or dictatorship normally has.
What's interesting is that human's won't need to change drastically to implement LIG. All would be required for LIG to be implemented would be a majority vote, and then to actually carry out the steps. The steps required by LIG have actually been carried out before, just not in this exact fashion or order. It would require setting up a company, and dividing shares of profits to the citizens of the nation (I'm not an expert in what this requires or if other steps would be required to make this happen). In all respects, it would act like any corporation today, the main difference being that the citizens of the entire nation will serve as shareholders. So its not really as drastic as it may sound initially.
I can't imagine how this could turn into something similar to communism, since that would require a charismatic leader that rallies the populous to overthrow the establish government and take over all sectors of government, making him their supreme ruler. LIG will not deal with any sector of government, whatsoever. LIG is limited to just securing the natural resources of the country, and providing the profits procured from normal business operations to the shareholders, the people.
I am not entirely sure if this has been spoken of yet, but transparency could be fairly easily attained through the internet, and so I could imagine that as a public company owned by the populous of the entire country, they would happily post all the details of their business. Im not a CEO of a company, so I don't know if that would be an awful idea, but it makes sense to me because they would only have to compete with international markets and not domestic markets.
In summary, your friends and family members have not understood the core concepts of LIG, which as I have explained here, are not as drastic or scary as they make it out to be. Im not the best talker, but I will just share what I can. Try to be very calm when they do get upset, or scared, or angry or any manner of agitation or disturbance. You would need to slowly but surely explain to them what LIG really is, and you could start by asking very simple questions to find out how much they already know. Perhaps they already read stuff online. After you have established what they do know, you can work with them to expand their knowledge to include what you know, making sure they get it every step of the way. It may help to give silent moments or pauses that allow them to calm down, and take a deep breath.
Hope this helps!