Why won t a credit union accept me as a member for deposits if my credit is frozen?

Because your credit report is frozen. Since it is they can not do so. You can unfreeze it, or not get an account. Your choice.

They want to pull a credit report and the freeze won't let them.

They use credit reports for identity verification. They don't need to know your credit score, but they do need to know that you are whom you claim to be and are not stealing someone's identity.

I guess I don't understand your reluctance to temporarily unfreeze your credit reports so that the credit union can check it. Unless you are trying to hide something, it should be a relatively quick process, after which you can lock it again.

Because if they can't check your credit history, they won't open an account.

Even though they are not extending actual credit to you, if their policies include checking a credit report before opening an account, then it is their policy and they have every right to refuse to open an account for you until they can check your score and credit history. This type of credit check would be considered a "soft pull" and would not impact your actual credit score.

It is perfectly legal. There are also a few other situations that could refuse service to you based on not being able to check your credit reports. If you try to rent an apartment or house, many landlords do credit checks also. You could be refused an apartment just because they couldn't check your credit report.