By putting someone on a cholim list you are asking the tzibur to daven/ say tehillim on their behalf. How sick does someone need to be for it to be appropriate to put them on such a list?
My late Rav, Rabbi Gedaliah Anemer, zt'l, founder and Rosh HaYeshiva of The Yeshiva of Greater Washington D.C., held that mishaberachs should not be said for those with chronic illnesses that are not life threatening at present. He said we don't want to "drey G-d's kup" (i.e. bother Him) with prayers for people who are going to have their illness for years to come. For example, he cited diseases such as MS and Parkinson's. I'm sure he was also concerned about tircha l'tzibur (a strain upon the congregation) by making them wait through a long list of names on the mishaberach list. I generally limit my contributions to my shul's mishaberach list to friends and relatives with life-threatening cancer or other life-threatening diseases such as a severe stroke.
Sheilas Yaavetz 64 - column starting ונ"ל טעם discussing praying for a sick person on Shabbos, says that one should only pray for an ill person, whose illness has taken a turn for the worse.
לכן אין לבקש על החולה אם לא תקף עליו חליו
His basis is Tircha D'Tzibura, which as you see we do not Daven 18 Brachos in Shemona Esrei on Shabbos.
אלא משום טורח הציבור אין מתפללין בו י״ח רק ז׳ ברכות, דהיינו משום שנצטוינו לענג השבת, ושלא נאריך בו בבקשתנו כמו בחול, האי הוא טירחא דצבורא
He goes on to say that one should not pray in an individual way nor with a Mi Sheberach it is all forbidden.
ולא שנא דרך כללי, או פרטי כמו שהוא הנוסח דמי שבירך , הכל אסור
However he says (this is printed over 200 years ago) we have a problem instituting this, as this has been the Minhag for a while.
אלא שאין כחנו יפה למחות מאחר שכבר נהגו משנים קדמוניות
This question and answer was specific to Shabbos. Perhaps during the week where there is more Tircha D'Tzibura (as people have to get to work) it is the same or perhaps during the week where we Daven a regular Shemona Esrei, Tircha D'Tzibura does not apply. Either way I imagine the line אלא שאין כחנו יפה למחות מאחר שכבר נהגו משנים קדמוניות would apply on weekdays too.
Could the guiding principle be Hillel's "That which is hateful to you, do not do to your neighbour"?
If you would be happy to use your precious time to daven/ say tehillim for someone with that level of illness, then it's reasonable to be put on the "the cholim list" for it.
But take care, making the Community wait (eg for a MiSheberach) is not a minor matter.
There is a gemara in Brachos 45b where Rava would not tell anyone the first day he was sick, so as not to ruin his mazal, on the second day he would tell his attendant to go announce his sickness so that people who love him would pray for him and so the people who hate him would be joyous which would result in Hashem having pity on him. A win win situation.
He didn't seem worried about the tircha for the people who would be praying for him.
In fact, any mitzvah along these lines of chessed such as bikur cholim, hashavas aveida, helping with a burden don't come with a clause excepting someone who finds themselves inconvenienced by the need to help.
And don't forget that lost objects getting returned with simanim was explained in the gemara as being a deal Jewish society accepted upon themselves so that today I return your object to you, and tomorrow You return mine to me. A Mishebeirach for cholim is a galgal hachozer.