I currently have a billing dispute regarding my credit card / personal line of credit / home equity line of credit. While the dispute was under investigation, the credit union reported my account negatively to the credit-reporting agencies. Can it do this

No. Generally, if you have filed a proper billing error dispute, the credit union cannot not make (or threaten to make) an adverse report to any person about your credit standing.

The credit union also should not report that an amount or account is delinquent because you failed to pay the disputed amount—or related finance or other charges—while the investigation proceeds.