The organization I work for has told me I cannot go to my 12 step meetings

You definitely want to make sure not to inadvertently create an inappropriate dual relationship with a client. 

In fact, it is not uncommon for state regulatory boards to determine that a clinician and client being in the same 12 step group is professional misconduct. 

You might want to consider attending a 12 step meeting that is located in a different community than the one you work in.  Another option would be to look for one-on-one or small group recovery support.

It is good to hear you are serious about your sobriety. Maintaining confidentiality and professional distance while living in a small community can be difficult.

There are alternative programs to support your sobriety online. They offer an extra layer of privacy compared to in-person meetings. You can still have social contact with anyone you know locally from previous 12-step meetings without putting your job at risk. It is essential to have friends who can enjoy time together without substances.

I worked for an organization that had a similar policy, although I'm not aware of it ever being enforced. Most of the employees were in recovery and active in 12-step programs. It has always been my personal practice that if I am present at a meeting and encounter a current client, I will leave. No questions asked. If I encounter a former client, I may decide to stay, depending on how involved I was in the treatment of that client, but I will not share during the meeting to avoid any inappropriate self-disclosure. I live in a relatively large city with a lot of groups, so it's possible to find meetings where I don't run into clients. This can be much more challenging in a smaller city. I understand that you don't work directly with peers in substance abuse treatment, but we know that many of our clients with chronic mental illness also have chemical dependency issues. Therefore, it is possible that you might encounter them at 12-step meetings. Perhaps you could try online meetings or consider driving to an adjacent city or town to attend meetings?

Seems you would benefit more from legal guidance than from therapist advice.

For example, I imagine policy must be presented in writing to the prospective employee prior to signing a contract of employment.

If you were not  given in writing the organization's policy of employees not being permitted to attend meetings, then I doubt the organization can hold you accountable for policy which you never were informed existed.

There are workplace rules and regulations which your matter may be protected by.

Since attorney fees are high, first look on your state's website for any agency your state government has which monitors employee rights in the workplace on being informed on policy.

If you are in the right, as to having the right to not follow policy about which you never were told, then the next point to consider is whether or not to take any action based on your finding.

Being legally in the right doesn't guarantee your workplace will be happy to accept they are wrong.

The next step is to consider your own peace of mind working for an organization which essentially believes violating your civil right to free association, is ok.

You may decide on a longer term plan on leaving this place.  Usually when an employer does wrong in one area, they are also doing wrong in other areas of the workplace.