Back at university, I remember one of my teachers told me that "as for something" carries an undertone of disinterest while "as to something", less used though, is a more neutral way of refering to something.
Is she right? How about other expressions like regarding, concerning, as regards, or simply for? Which one is used most frequently or informally?
I'm going to disagree with your teacher. While we do commonly express disinterest or disdain for something by saying as for that*, the phrase does not inherently carry those sentiments. Similarly, one could put sarcastic emphasis on as to that to express the feeling that your teacher says comes with as for that.
As with so much in English, context, stress and intonation must be known to grasp the nuances. It's entirely possible to use both as for that and as to that in a completely neutral, dismissive or even excited fashion.
I'd say that the simpler terms regarding, concerning and for are more staunchly neutral than the other two phrases. Absolutely they can all be inflected negatively or positively, but the as phrases (including as regards) naturally draw more attention because they're more verbose and come off a bit more formally (though all of these are appropriate in formal English). Because they're marginally stronger and thus set topics apart slightly more, it requires less work to shift their sentiments. Conversely, my voice would need to ooze sardonically to make it explicit how little I value the topic if I prefaced it with regarding.
In my experience, for, concerning and regarding are the most common of the terms from the question in informal registers. Though, again, they are fine for formal use. In colloquial conversation, you are also likely to encounter about [that] or [other topic], that's...; these are not formal expressions. Since informal language is more fluid and flexible, the emotions carried by these terms are also considerably more plastic.
*Aside: swap the order of the two important bits of this clause and note the drastic change in meaning! As for that is commonly said to express disdain or disinterest.
"As to" is used significantly less than "as for," and they don't necessarily mean the same thing. According to the Merriam-Webster dictionary, "as to" can be defined as:
As for/About
According to/By
The first of these is more frequently used than the second. Being a native English speaker, I don't recognize any difference between "as for" and "as to," but they are used in different kinds of sentences. "As for" is often used to either start a sentence or add onto a sentence:
"My wife and I are well. As for our work, it is not going well."
It can also be used (formally) to connote similarity:
"For Hawthorne, as for Borges, his writing was a reaction to his cultural situation."
As to, on the other hand, can be used in the ways stated at the beginning:
"The programmers were at a loss as to how to explain the error."
or
"The blocks were graded as to size and color."
"Regarding" would not typically be substituted for "as for" or "as to":
"As for the mayor, he can pay for his own dinner."
-> "Regarding the mayor, he can pay for his own dinner."
While grammatically correct, that sentence is a rather atypical form, so "as for" would still be more appropriate. However, "as for" can be defined as "regarding," even though the words aren't very interchangeable in common English. "Concerning" would be slightly more appropriate (though "as for" still sounds better):
-> "Concerning the mayor, he can pay for his own dinner."
Finally, "as regards"/"as respects" is another way of saying "in regard to" or "as compared to."
I hope that answers your question, but comment if I need to explain something better.
There is a contrast, but it is subtle and not part of the meaning of the two phrases, but part of their connotation (the cultural or emotional association) that comes from how people have often used them in the past. The difference in connotation is pretty weak though, so I think your teacher was overstating the the importance of choosing one over the other.
The relevant difference is:
For example, two uses that magnify the connotations:
This is how the two phrases are often used: to emphasise your respect for ("as to") or dismissal of ("as for") the subject. So when you use them with a neutral statement, "as to" could be understood that you are implying you respect the subject or people connected to it, while "as for" could be understood that you want to imply (without saying) that you feel dismissive of the subject:
The implication is fairly weak though, and can easily be overridden by the tone and meaning of the surrounding sentences, or by how you write/say the rest of the sentence that starts with "as to/for":
Because the effect is fairly weak, it's also often going to be more important that one is formal and the other less formal. In a formal environment, "as to" will usually be more suitable regardless of whether you respect or disrespect the subject, while in an informal situation "as for" will be preferred so that you don't sound "stiff".
A final note: using the wrong one will not often result in a misunderstanding, because the surrounding sentences will usually more strongly communicate your attitude on the subject than the "as to/for" choice. More likely, using the "wrong" one will only result in a native reader/speaking believing that the sentence sounds awkward in context.
