I had this happen to me over 20 years ago. They were Christians. I asked them what Biblical basis they had against homeschooling. They had nothing which told me it was just opinions I was dealing with. I thanked them for their concern and told them we felt homeschooling was the way the Lord was leading us. I explained that even though it was different than what they preferred for us, we were going to follow as the Lord led. If they sincerely felt we were in error on this, then to please pray for us and trust God to do that work in our lives.
That worked!
It took the focus off of coming to us with their worries and sent them straight to the Lord.
I made up my mind to obey God and not let the voices of others distract/hinder me even for a moment from where He was leading. God blessed that.
My oldest graduated at the top of his college classes. At 22, he was the youngest person working where he works as the sysadmin over two industrial plants. He makes VERY good money, just got back from a two week trip in Europe, owns two cars, has paid off most of his college loans, has a good start on his retirement fund, and at 23 years old purchased his own home.
When she was 19, my now 22 year old was given a raise and made assistant manager over the store where she worked after being cashier for two months because of her work ethic and accuracy. She has a new job that she has been working three months and has already been moved up with raises twice. She is on her way to buying her own home.
I have a 13 year old who is almost done with high school through a regionally accredited online course.
There's nothing like success to quiet the dissenters.