At issue there is if the Espinoza and Reid complied with the money transmitter laws of the state of Florida, not if the transaction was prevented. (And the defense may be able to beat the case on that point). The transaction isn't prevented if the parties involved complied with the state MTL regs, which admittedly are burdensome.
It doesn't pass 1st Amendment muster if the regulations are so burdensome as to effectively prevent the transaction.
It's similar to arguing that 1st amendment rights allow a political contributor to donate anonymously, which seems counter-intuitive.
The Supreme Court has long held that anonymous speech is protected under the First Amendment.
The premise for these two cases is very different. Florida v Espinoza and Reid involved an undercover agent attempting to purchase $10,000+ in bitcoin which would be used to buy stolen credit card information (not to mention the issues raised in armspir's above post). The case states the purpose of the bitcoin purchase was known by Espinoza and Reid. While it is possible for Espinoza and Reid to beat the charges for other reasons, I can't see how it would fall under the first amendment.
As far as I know, neither Espinoza nor Reid claimed that their actions were protected under the First Amendment. However, someone buying a similarly large amount of bitcoins could claim that their intended use of the bitcoins was for a constitutionally-protected activity, rather than for the purchase of stolen credit cards.