If you are on long term disability with a private insurance provider can you have an Etsy online business without risk of losing your benefits?

Typically, LTD policies do require that specific income is disclosed to the insurer, and they may be able to adjust your payments or end your benefits if you are 'working'. You should review your LTD policy carefully to determine your rights before engaging in such business, so you can get a better understanding. Unfortunately, each policy is different so there is no one-size-fits-all answer.