Tara Duncan
You have mentioned some of the issues with biometric authentication, i.e. storage, security. On the bright side you have an AGENT (Union) to protect your interests. This assumes your agent is familiar with the legal and technical implications of this emerging practice.
Some of the things I might want to know before opting in would be: How is the data stored? What is their contingency plan when it fails? What protections are in place to prevent the data being accessed by third parties? What happens if I don't agree? What is done with the data if I'm no longer employed by the company (i.e. will the data be deleted, retained, etc.)? If a regulatory body/third party requests the data will it be made available to them?
As Scott mentioned, if you have not signed an employment contract indicating you have agreed to this practice you can decline; however they can fire you for non-compliance.
Most people will agree to this without thinking, which appears to be the default state of most humans these days. If qualified your union should be representing the interests of its constituency -- if qualified. It should also be noted that the union optimally represents the majority of its members - if no one has an issue, the union usually doesn't as well.
The last consideration should be how committed you are to not disseminating your biometric information. If you are not willing to quit your job, or have no other options, it's pretty much a non-issue.