Oooy? So some say there are schools out there that do not sparr at all?

Some don't at all and more don't spar until the student has some rank and actually knows how to use some techniques and knows how to evade attacks. There is little use having two white belts go at each other wailing. Might just join the local bar room brawl.
It is also a misconception that Mcdojo don't spar. Mcdojo often are highly tournament motivated and so point sparring is of the utmost importance. As a matter of fact I found quite the opposite is true. Mcdojo spar a lot because it is easy time for the teacher. He does not have to think why this student can't do this technique and how to fix it. Just let the students go at each other and stop the match when the students get too rough. To me that is an easy class to teach.
It is also a misconception that Aiki or jujitsu schools don't spar, unless you think sparring is only exchanging blows rather than exchanging techniques, any techniques. Fighting is not just hitting. Sparring in those arts is much more dangerous though because if your timing to roll out of a technique is off even by a little you can get something twisted and injured really easily. It is not as easy as tapping when it hurts. Many techniques use the opponents momentum and you can not just simply stop them once they get going so you have to know how to get out. It's like trying to get off a ride at an amusement park safely right now when it is in full motion.

Usually those are mcdojos

There are many schools that spar falsely. They practice point sparring.

Depends on your definition of "sparring". For instance, one of my Goju teachers was of the mind that we shouldn't do free-sparring because the techniques were "too dangerous" but we did drills that were basically no-contact one-step sparring. In Wing Chun, we didn't do what would normally be recognized as sparring, but Chi Sau serves a very similar purpose, though it tends to be hyper-focused on a specific skill set.

I don't think most Aikido, Hapkido, or classic Jujitsu schools do free-sparring. Most "ninjutsu" places don't. I can't imagine how you would free-spar safely in a Kobudo class. I don't think most Silat classes spar. The list most assuredly goes on.

that would be mcdojo's.
its not most schools but there are a few., and it has nothing to do with the style, it has to do with the instructor of the area you are in. people that claim its a specific style are clueless.
for example my tai chi instructor even has sparing in his school, and it was full contact as well, at least for the advance students

edit:
callsign in kobudo, with my partner an a very select few senior students we do free sparing with real weapons.

as for the rest of class they have padded or foam weapons for sparing.

edit
jas key that is completely incorrect,
first off there are many traditional schools that do full contact free style sparing
secondly that is not the difference between and mma.
third traditional styles do evolve. if you take shotokan for example the shotokan taught today is not the same as the one taught in the 1950's nor is it the same as when it was first taught in 1936.
even in karate in general, there were techniques add that were not in the karate 50' years ago or a 100 years ago.

All styles have sparring of some description, no matter how much of a stretch it sometimes takes to call it sparring. all styles also have that group or school of people (big or small) who spar in a way that can be considered 'good training'.
Aikido for example has the Tomiki branch.
Most of the Aikido community label them as loons until they're asked to find full-contact training in their ranks then the Tomiki videos start flowing as an example of Aikidoka training properly.

dno

There are schools out there like that. And not only McDojos. There are arts who utilize very light sparing, then you have point sparing which I think is equally ridiculous. Point sparing is when two people face off. They spar until the first one hits and then they start over. So one hit and then it's over. A lot of styles also just practice their techniques on a 100% compliant opponent.

I think the word sparring needs to be defined first. As the “non-traditionalist” defines it, sparring must be full(or close to full) resistance without too much restrictive rules that forces the fighters to act in certain way.

As an example Aikido’s free flow drills wouldn’t be considered sparring due to lack of resistance. Wing chun’s push hands wouldn’t be considered sparring because the rules restrict the fighters from straying too far from the techniques they are trying to reinforce. In both cases these are drills and these styles acknowledge it as such.

However things like point sparring, grappling purely for position, and such should be considered a drill as well, but many would define these as sparring. If people took out these drills, we’ll find that most people rarely or never spar at all.

Also you’d find that “non-traditional” martial arts are usually as ancient as the “traditional martial art”. The actual line between traditional and non isn’t the history, but usually the full resistance sparring with not so restrictive rules that allows for continuous evolution of the martial art.

Thus the claim that traditional martial art doesn't usually spar.