Even sites that do require ID don't necessarily require this selfie crap. I'm verified on Coinbase and never had to do that. I don't believe you need a selfie on Gemini either. These are just arbitrary requirements from Bittrex (or rather probably their 3rd party KYC provider). The law doesn't require it.
You can even not comply with the KYC but you will have a limited fund transfer for a day/year. As of the selfie holding your ID, it is just an extra layer of protection for the name holder, since identity theft is rampant in the internet. It is to make sure that you are actually the one on the picture and the one using their platform. Anyone can take its meaning the opposite way, but well, the thing is if we want to use their service, we need to comply with their rule.