Texas law defines a "business pursuit" as incorporating two elements: "(1) continuity or regularity of the activity, and (2) a profit motive, usually as a means of livelihood, gainful employment, earning a living, procuring subsistence or financial gain, a commercial transaction or engagement." Allstate Ins. Co. v. Hallman, 159 S.W.3d 640, 644 (Tex. 2005). CMLP has identified no Texas cases interpreting this test in the context of online publishing out of the home (or elsewhere).
As a general matter, however, Texas courts recognize that "hobbies" are distinct from business pursuits. One court has defined a hobby as "a specialized pursuit, such as stamp collecting, painting, or gardening, that is outside of a person's regular occupation, usually done in a non-professional way as a means of relaxation during leisure time." United Servs. Auto. Assoc. v. Pennington, 810 S.W.2d 777, 779 (Tex. App. 1991). In that case, the insured, a car salesman, bought a horse in order to experiment with new race training methods. The court held that the jury was entitled to view this as a hobby and not a business pursuit, even though the insured admitted that he would have liked to turn the activity into a business in the future.
Therefore, if you live in Texas, you have a good argument that your online publishing activities are not a business pursuit, so long as you can characterize them as a hobby. It will help if your primary motivation for publishing online is not financial gain, and you have other employment.
Note that specific language in a policy might lead a court to a result different from the overall state trend.