Well, yes, they have the right to strike in the sense that police can't force them at gunpoint to go to work. But pursuant to the Taylor Law, and as stated by Bloomberg, they will be fined two days pay for every day they strike, and their union is being fined $1 million per day. Some 'right'!
If the Taylor Law fines workers and subjects them to jail time for exercising their right not to work, it is unconstitutional. The MTA's remedy is not to "force" workers to work through fines and jail, but to fire them if they don't work.
A contract is a contract.
These people are breaking the law. And to top it off - it's for more pay than there is money to pay them...
This strike represents the #1 reason Unions have become obsolite and bad four our country.