I don't know, I might just be paranoid, but I worry that a family with children that receives food stamps might be put on some sort of list that makes them more prone to visits from the CPS.
And I will also admit, I fear the scorn from the community. I know this is not a legitimate reason not to do it, and it wouldn't stop me, but it's an aggravation. We live in a small town. I can just hear it now. Why don't they just put their kids in school, she's too lazy to work, why should we have to pay for their food, etc etc etc.
This is not actual advice, just sharing my thinking. I'd hate to be wrong. But I think that CPS does not come out to anyone's house without there first being a referral of some kind, such as from a concerned neighbor or teacher, or the police have discovered something. As far as I know, CPS has to be "invited" somehow.
There are very many people receiving food stamps and other governmental aid. CPS doesn't have the resources to regularly visit such people. The biggest trouble one might expect to get in, is getting caught lying about income. But I think scads of people lie and get away with it all the time.
The fact that you homeschool combined with economic need might raise governmental interest. I know that some states force homeschooling families to submit to certain kinds of surveillance. Are you subject to anything like that now? Do you have to file reports or submit to home visits?
I don't think you are being paranoid, not in this landscape. If you live in a small town, then employees that work for the agencies involved will know your personal business. And they may gossip or find ways to interfere.
Perhaps a rule of thumb is to consider all you've experienced since you began homeschooling. If thus far there's been no intrusiveness, then you may not have any problems as long as you qualify.
Let's face it, more and more families, even two-income families, are getting hit hard with the prices. My wallet is bleeding like a stuck pig, and I have no dependents. In such a circuмstance, you might stick out or call attention to yourself less than you might expect. There's another reason for your plight, and certainly not your decision to homeschool. In fact, homeschooling saves money.
Your second concern is also known as The Cross. You may very well be forced to taste bitterness if you go down this path. Think of the Holy Family. The bitterness of poverty, of exile, of shunning, of being hunted by the authorities, of living among the Egyptian heathens.
But again, what has been your experience in your town thus far? Have you already drank from the cup of the uncharity of others? Or have you been left in peace? I think it is reasonable to expect that the level of reactivity to your lifestyle and fidelity to God will continue in kind and degree as you move forward.
This goes without saying. Commend yourselves to the Holy Family, and ask Them to guide and protect you. I will add you to my prayer intentions bucket.