Religion

You also can't make it out of a hospital without an actual temperature reading on your chart.

The "normal temperature" of 98.6 was established in the 19th century using axillary thermometers that would not be accurate enough for modern use.
https://www.realclearscience.com/blog/2015/08/the_average_body_temperature_is_not_986_degrees.html

Normal temperature ranges by person, time of day, exercise, outside temperature, sex etc.
https://www.webmd.com/first-aid/normal-body-temperature#1

A 1992 experiment found that average temperature is 36.7 C and suggested that a fever begins at 37.7 C rather the tradition 38 C, but the range they found in healthy persons was from 35.9 to 38.2.
https://www.ncbi.nlm.nih.gov/pubmed/1302471
http://saidsupport.org/normal-body-temperature-periodic-fever-syndromes/

A 2008 experiment suggested that older people had lower body temperatures therefore, lower fever points should be used.
https://www.ncbi.nlm.nih.gov/pubmed/18705705

And what exactly happens in the body at 37.9, 38, 38.1 or 38.2 that is so different? Probably very little, but we have to draw the line somewhere, to catch as many potentially ill as possible and avoid saying healthy people might be sick.

And we haven't even considered hypothermia which begins below 35 C. But that doesn't happen so much, so medical charts don't need to state that a person with a temperature of 37 C is ahypothermic.

And there is still a matter of definition. I consider myself to "have religion" because I do participate in some religious rituals, but that's not the same as being a theist. Buddhism is generally considered to be a religion, but Buddhists on this site have said that it is not a religion. Buddhism officially has no gods, but many Buddhists have in fact worshipped gods as part of some traditional practice, or they may perform acts of worship or ritual in front of statues of the Buddha, who is not a god. Buddha himself said he was agnostic, but according to you, 2500 years later, he must have been an atheist?

Some religions, like animism and shamanism, may not have any gods at all, just various spirits that are in a continuum with human beings and animals. Are these religions atheistic, agnostic, theistic, or just have no idea what we are talking about?

And all of that is just for the formalistic definition of "fever" in medicine. If we were looking at temperature from the point of physics, chemistry, microbiology or forensic medicine, we'd have a whole bunch of different scales.

And to wrap this all up, if a person with a fever is febrile, and a person without a fever is afebrile, what do you call people without thermometers or with broken thermometers? What do you do if you have two thermometers and one gives different readings from the other?

I've only scratched the surface of why I think even a simple thing like a fever is really non-binary (even if we have to make it binary for diagnostic flowcharts). I just don't think in binary. Sorry. I just don't.