I'm glad you posted this. I thought very seriously about homeschooling my children back in the 90s. I can only speak to my experience. The only materials I could find were based in religion.
My purpose in homeschooling, or thinking of it had nothing to do with religion. Again, I literally could not find materials without a religious approach. I wanted to homeschool because public school wasn't addressing the needs of my boys.
My boys were very bright. I was told my my oldest son's kindergarten teacher to stop teaching him stuff because he was becoming annoying. Ummm, no.
I wanted to let my boys learn at their own pace, which was faster than the average. I couldn't get my hands on secular materials at the time. I was looking to educate, not indoctrinate.