It's understandable how people can get into the habit of thinking of the state in which they live, and probably also the neighboring ones, to which they are prone to regularly address postal mail, in terms of the postal abbreviations.
Though the addressing of mail using the postal abbreviations is ubiquitous, it is still a rare person who knows all fifty of them. When familiarity is not universal, use in text can leave a significant part of the audience wondering if AL refers to Alaska or Alabama.
So, it is generally only correct to use a postal abbreviation as part of an actual address block (on an envelope, at the top of a letter, conveying a third-party's address in the body of a letter, anywhere when street/city/ZIP code are present, etc.)
Our advice, for the sake of simplicity, is that within text or anything resembling traditional sentence structure, you should write out the name of the state.
If you're just looking for a basic instruction, you can probably stop reading now and go about your day.
On the other hand, if you're interested in some of the qualifiers and digressions, continue:
In the matter of postal abbreviations, different style manuals handle these things differently. The Chicago Manual of Style (CMOS) prescribes the advice that Write and Polish dispenses above. It is a clean and straightforward solution with nothing to look up or memorize.
However, The Associated Press Stylebook (AP) has a set of abbreviations (and non-abbreviations) that it adopts for each state -- the so-called "traditional" abbreviations that pre-dated the postal system's two-letter designations. The majority of newspapers follow AP style, and these handles do clearly convey the necessary information. However, the traditional abbreviations follow no simple rule, like "three letters, first capitalized, ending with a period." They're each their own thing, including the eight that are never abbreviated! So, for the average person writing everyday business or personal material, to follow AP, you would need to refer to a list each time unless you'd learned them.
Now, Write and Polish, being concerned about the aesthetic appearance of information on the printed (or rendered) page, writes the state name in its entirety in text AND IN ADDRESS BLOCKS. Though the postal system (their optical readers, actually) wants universal use of its two-letter codes, at present, our preference for what we find to be a more elegant look does not interfere with delivery. We will also admit, when dealing with our own materials, to a streak of obstinacy in the face of government-instituted homogenization!
This W&P choice illustrates what is known as "house style." How material is presented can support, detract, or be neutral with reference to the brand and the organization's culture. A business or institution will often choose a major style manual to act as a "base" for its written material, and then supplement it with brand-specific requirements and other exceptions that constitute its own, hopefully distinct, style. House style should still be consistent with understanding, but allows for leeway in a variety of areas.
For example, as of this writing, explicit direction to include or exclude the comma before the terminal conjunction in a simple series has become a "house" style point, as in:
We color-coded our edits in red, blue, and green.
or We color-coded our edits in red, blue and green.
The first presentation was once de rigueur, but has largely gone by the wayside as unnecessary and redundant. For those who feel strongly about retaining that comma, however, spelling out the expectation in an internal style manual ensures that it is done consistently throughout the organization.