Thanks to everyone who has posted thoughtful comments to this interesting thread.
In answer to the OP's questions: my family and I definitely aren't looking for any tax cuts from the government to support our homeschooling. And, just like it's never alright to make broad brush negative statements about Muslims or blacks or Jews, I can't think of any good reasons to justify why it would be okay to hold on to negative stereotypes of *all* homeschoolers, as clearly each family is different.
While I can understand that from a societal perspective some people might think it would be desirable to have more safeguards and regulations in place to monitor homeschoolers, we are personally very grateful that our state has not made any efforts whatsoever to check up on us since we pulled our daughter out of public school a little over a year ago. A few days before we left the US in 2016, I went into my daughter's elementary school and told one of the ladies in the office that we were planning to travel to Japan over winter break and weren't sure if/when we would return. A little bit surprisingly to me, that didn't seem to faze the office lady, at all. She just asked me to sign my daughter out of school and told me that as soon as we knew the address of our daughter's new school to let them know and they would forward her records. That was the last we heard from the public school system in the US, and, TBH, we're quite happy with that arrangement.
Since December, 2016, my wife, (now) nine year old daughter and I have been traveling slowly around the world, usually staying a month, or so, in each city/country we visit. So far, we've tried various strategies to educate our daughter as we travel. Early on, we enrolled her in a public school in Japan for a month. Then we tried some homeschooling, both with and without a curriculum, for a couple of months. Next, we enrolled our daughter in a private English language international school in Vietnam for 2.5 months, so she could spend some time around other kids her own age.
For the past six months we've mostly been Worldschooling our daughter, i.e., not explicitly teaching her any particular school subjects, but helping her to learn from the experiences we've been having as we travel. In the past year, both my wife and I have read dozens of books together with our daughter, and our daughter has read dozens of shorter, easier books herself. She's an excellent reader, far above grade level, and her comprehension of the books we read seems good, as well. Right now, my daughter and I are reading Steinbeck's Of Mice and Men. My wife and daughter have read the entire Harry Potter series. My daughter and I recently finished reading the Hobbit. Before that we read Animal Farm. And she just recently turned 9 years old.
In addition to reading lots of books, we watch movies together as a family, sometimes on Netflix and sometimes in a theater, and we talk about the movies with her afterwards. We're constantly talking with our daughter, and she's constantly listening to my wife and me talking to each other and to people we meet during our travels. Our daughter hears us talking about racism, sexism, #metoo, Nazis, white supremacists and Antifa. She hears us talking with national park rangers about invasive species eradication plans, plate tectonics, earthquakes and volcanic eruptions. She hears us talking with people we meet on the road, explaining to them that, "No, we did not vote for Donald Trump. No Americans aren't all racists. And, no we're not all fat." Using the Google Earth app on my phone, our daughter can easily point out all of the places we've visited in the past year. Ask her to find Kuala Lumpur, and she can easily spin the globe around and zoom right in to the correct spot on the west coast of Malaysia. Japan, Hong Kong, New Zealand, China, Cambodia. Ask our daughter where they are, and she can find them all on Google Earth and tell you a little bit about her experiences in each country.
Reading some of the comments above in this thread started to make me worry a little bit that maybe we were doing a disservice to our daughter, because neither my wife nor I are certified, professional school teachers with years of experience at modern pedagogical methods and techniques, but the more I thought about it, the less I was worried. Pretty sure, our daughter is going to be just fine. If and when she goes back to a regular public school somewhere in the US, someday, if there are any gaps in her knowledge, my wife and I can easily help her to get back up to speed in whatever areas she may be lacking. Probably, though, our daughter will be ahead of many of her classmates in some areas, as well, so hopefully her weaknesses and strengths will even out and she won't have to struggle too much.