That turns out to be an important legal question, at least in New York. Here's the text of N.Y. Labor Law § 201-d:
1.... “Political activities” shall mean (i) running for public office, (ii) campaigning for a candidate for public office, or (iii) participating in fund-raising activities for the benefit of a candidate, political party or political advocacy group ....
“Recreational activities” shall mean any lawful, leisure-time activity, for which the employee receives no compensation and which is generally engaged in for recreational purposes, including but not limited to sports, games, hobbies, exercise, reading and the viewing of television, movies and similar material ....
2.... [I]t shall be unlawful for any employer [to discriminate against an employee or prospective employee] because of ...
[a] an individual’s [legal] political activities outside of working hours, off of the employer’s premises and without use of the employer’s equipment or other property [except when the employee is a professional journalist, or a government employee who is partly funded with federal money and thus covered by federal statutory bans on politicking by government employees] ... [or]
[b] an individual’s legal recreational activities outside work hours, off of the employer’s premises and without use of the employer’s equipment or other property ....
3. [This section] ... shall not be deemed to protect activity which ... creates a material conflict of interest related to the employer’s trade secrets, proprietary information or other proprietary or business interest .... [Exceptions related to some government employment, and a minor exception related to private employment, omitted.]
So can a New York employer fire an employee for offensive statements on the employee's blog (assuming the blog doesn't carry any advertising, the employee blogs from home, and the blogger doesn't reveal any trade secrets or confidential information)? The protection for political activities is quite narrow -- general statements on public issues wouldn't qualify, unless they're said in the context of a candidate campaign or fundarising activity for a candidate, party, or advocacy group.
But the protection for recreational activities seems quite broad: It covers a wide range of "lawful, leisure-time activity" (so far blogging qualifies) "for which the employee receives no compensation" (that's why we're assuming there's no advertising) "and which is generally engaged in for recreational purposes, including but not limited to sports, games, hobbies, exercise, reading and the viewing of television, movies and similar material."
So is blogging "engaged in for recreational purposes," as a sort of "hobb[y]," or the flip side of the "reading and the viewing of" media material? Or is blogging for the purpose of expressing your views something other than recreation -- perhaps a form of ideological advocacy that's deliberately excluded from the narrow "political activities" provision, and thus not meant to be included in the "recreational activities" provision?
No cases that I know of so far on this subject in New York; but it still struck me as an interesting item to air. (I have a problem on the subject in the second edition of my The First Amendment and Related Statutes casebook, and I'm writing the Teacher's Edition discussion of that problem right now.)
I am curious about the NY law you cite though ... In this context would pure issue advocacy of a, "Vote No on Proposition 31" type NOT be "Political Activity?" That would seem to be a pretty odd result from my perspective.
Although a Texan with no New York legal exposure, I would imagine that job actions short of termination for these types of activities would seem to be possible, but firing someone for blogging would be a much dicier proposition.
Adultery? A recreation for some, a political statement against repressive monogamy for others?
Blogging about sex?
It seems there could be a reasonable legal definition built around the specific contents of the blog. If the blog is called "Someone-kill-all-democrats.blogspot.org" and consists of likewise political material, then it would seem reasonable for an employer to distance themselves from that person through firing. Working our way back from that extreme point it seems as though society could reach a reasonable clear black-and-white line on legality.