Is it legal for my former employer’s bookkeeping company to refuse to give me my W-2 because they were not paid?

Well, technically, your W-2 form is that company's work product. They took the time and effort to generate it, so it is their right to demand payment for their work. You should contact your former employer and demand your W-2 from your employer. If the employer refuses or ignores your request, you can report that employer to the IRS because it is ultimately the employer's responsibility and obligation to issue your W-2. You should not have to deal with the employer's bookkeeping company at all.