It seems to me that in most cases our goal (those who are answering questions, mostly) is to help learners be able to use "English as she is spoke", that is, to use the language so as to understand and be understood by fluent speakers, whether in speech or writing, whether in casual, business, formal, or technical contexts, as each learner may need or want.
Learning "rules of grammar" is a tool to that end, not an end in itself. But in some cases it is a useful tool. A rule is often easier to learn and remember then endless special cases.
The question and some answers discuss the split between prescriptivists and non-prescriptivists . But in my view, the more fundamental split is between formalists and non-formalists. A formalist, in this context, believes that a useful set of rules of grammar define correct English. A prescriptivist is by definition a formalist. But there can be descriptivist formalists also. Such a person looks at current usage, and then attempts to distill it into "rules". Such a person believes that the rules change as usage does, but at any given moment there is a set of rules which define correct English.
The problem is that English usage is too complex for a useful set of rules to capture it fully. English is finite, and in theory a finite set of rules could capture its every nuance. But such a set of rules would be so large and complex that it would, I think actually be harder to learn and use than just memorizing every word and its special usages. It would also be a monster effort to formulate such a set of rules and keep it up-to-date. A Formalist acts as if we already have such a set of "perfect" rules. But we don't.
Rules of grammar that are usable cover the more common cases. They often miss edge cases and nuances, sometimes badly. Teaching the rules without teaching the exceptions, or at least that there are exceptions, will often serve learners poorly. They may fail to understand less common usages, and may sound odd to native speakers.
Many learners are formalists. They expect a clear-cut, often simple, rule for every case. Perhaps their other languages are closer to this ideal. Perhaps they have been taught by formalists, either in other languages or in English, or both. But this can leave them confused when a "rule" they have been taught or have deduced fails to correctly describe some usage.
Many people posting answers or comments on this site tend to write as formalists. They declare rules, and say that any usage contrary to those rules is "wrong". Sometimes the proposed rule is sufficiently widespread that any usage contrary to the rule will be unclear or sound odd to a fluent speaker. But sometimes the rule is better thought of as a guideline. For example, one poster recently denounced any use of a double negative as "wrong", even though many acknowledged "good" writers use certain kinds of double negatives ("not unlikely" for example) and some dialects make them a very common part of their usage. To teach such a rule as an absolute is not helpful.
Often summarizing a wide group of usages in a "rule" is helpful. But we have to be aware of the limits of the rule, of classes of exceptions, or at least that there may be exceptions, and mention those things when teaching the rule, in my view.
And when we use rules derived from grammar texts, whether "traditional" or "modern" we need to be aware of changing usage. A rule thought correct at one time may not correctly describe usage now. In many cases it never did, such as the "rule" about not ending a sentence with a preposition, or the "rule" against split infinitives. Or the "rule" that all conditionals belong to one of a small set of numbered types. There is correct usage that violates each of these rules. So any such rule must be mentioned with caution and caveats, if at all. At least that is my view.