I noticed that often when I appeal to common sense, people will want some background reference, or statistical or other evidence to support an opinion. — god must be atheist
Some rhetoric teachers recommend NOT appealing to common sense. For one, common sense is perhaps a good deal less common than we hope, and for two, it either doesn't mean anything in particular, or it means nothing. I don't care if you use the phrase "common sense" but it does have rhetorical deficiencies.
If you say something that somebody else doesn't particularly like the sound of, an easy negative response is to ask for evidence, or a reference. In many cases, we can cite actual evidence and give references for our statements, but it's a lot of trouble to track it all down. Everyone knows this.
If I say, "Gay is good." I have stated a personal opinion with which others can only respond to by stating their own opinions. So you can say "Yes, gay is good" or "Gay is not good." Either way, it's merely your opinion, and my opinion is merely mine.
If I stated that "The human species will be wiped out by 2200 because of global warming." I am making a statement which may be factually based, may be factually erroneous, may be misinformation, or may be wishful thinking. In this case, people can, should, and ought to ask for the evidence behind my statement.
I can't say, "Oh, it's just my opinion." I need to cite scientific reports that suggest that global warming from greenhouse gases will make life untenable by 2200, or that disease and starvation will wipe us out (because of global warming), or something else.
As it happens, I don't believe that we will be wiped out by 2200. I would expect to see population levels dropping steadily by that time, heading toward a new, lower, equilibrium level. Disease and starvation, massive flooding, hot weather, high humidity, bad storms, etc. will probably be the new normal. I believe there is some evidence that if trends continue, the environment which we are accustomed to will gradually disappear and be replaced by the one I just described.
The trick is to not make really bold claims without providing information (or a source, at least) to back it up. If you make a statement of shocking opinion, then you should explain why you hold that opinion.
People may (will, pretty much) still give you negative feedback. There's nothing anyone can do to prevent that. It goes with the territory.