Who are these hypothetical normal people who behave in a manner that coincidentally harmonizes with the philosophy of your choice?
I've never met a normal person. That doesn't really prove anything, since the number of people I've met is statistically negligible compared to the number of people who have ever existed, and this is a bit of an abuse of the word "normal" anyway. So... what do people mean when they talk about "normal people"?
I don't know, no one's ever told me. Everyone fairly close to average? (Average what?) The majority of majorities? People who agree with the speaker? Maybe we could poll everyone and say whoever thinks she's normal is normal, and vice versa. If we ended up with considerably more people answering "yes" than "no", this might even seem to be a valid method of sorting them out. But I suspect the percentage of humanity everyone knows is fairly similar to mine, so the comparison that they're making is based on equally insufficient data.
Let's suppose we work out the core aspects of human personality, and can compare people in each aspects in a meaningful way. The most primitive models I can think of, the four humors, uses a pair of dichotomies (say, extroversion and introversion) and is not very accurate. Myers-Briggs uses, I think, four axes, one for each letter, and I can't honestly say every other INTJ would get along with me. The more accurate the model, the more axes are necessary - I know of one that uses sixteen, and I imagine there are plenty of holes in it as well.
Quite a lot of these models have axes that are non-coincident, which just increases the total number further. And we'll have to consider that people with similar personalities don't necessarily agree, and throw in some ideological axes - traditionalist versus neophilic, judicious versus merciful, jack-of-all-trades versus master-of-one, et cetera.
Now - it seems reasonable to expect a plot of where each person falls on each axis to be bell-curve-shaped. Fair enough. Let's say a person with a normal level of some trait is one who falls within a standard deviation of the peak of its graph. Take all of our plenty-seven axes and superimpose their zeroes to get an array of over six billion individuals each represented by a single point in plenty-seven-dimensional space.
I would be quite surprised (note - this is the most subjective bit) if the bell curves on all these axes coincided so smoothly as to leave the majority of all humans within one standard deviation of every single peak. If they don't, which seems most likely, then normalcy has no objective meaning, if there's anything remotely objective about this entire idea when all is said and done.
It's a big internet, so I doubt all is said and done.