From a banker's perspective, two terms you guys need to understand that every bank has to operate under from a regulatory standpoint:
AML: Anti-Money Laundering
KYC: "Know Your Client"
I'll let you Google the various regs that the above two concepts bring to bear.
From a bank's perspective, if I allow my clients to transact in BTC, it holds similar weight from an AML/KYC standpoint to conducting foreign exchange (FX) trades with a client doing business with Russia, North Korea, Iran, etc...an extreme example, but you don't know fully who the counterparty is on the other end of the transaction. Because the market is not regulated, you could be dealing with the Dark Web, funding from a drug kingpin, a Russian businessman, or ISIS.
Money (USD) is "dirty" as well, but if I'm buying or selling stocks on a regulated exhange, there is less chance of a criminal backlash against the banks/customers involved.
Not justifying the banks' concerns, nor criminalizing all cryptocurrency participants....but while the current benefits are HUGE, there are possible risks that could rear their ugly heads at any time.