There is no general rule prohibiting the U.S. government from requiring registration, for example, with an email address, in order to provide government software or data. There would only very rarely be a constitutional or statutory prohibition on doing so.
This is not a question that is governed by a single law or regulation, however. Different statutory and regulatory provisions apply to different kinds of software and different kinds of data.
In some cases there are fees authorized by law or there are legal requirements that you identify yourself, or both, for example, in certain kinds of Freedom of Information Act requests.
There is other data that the U.S. government provides without a registration requirement (e.g. much of the data that appears on websites). Different agencies would have different requirements and usually there would be multiple kinds of data subject to different rules in the same agency.
For example, the United States court system maintains data bases of court records. But, some court records require special approval to access (e.g. limited to parties or to certain officials), while others are publicly available upon payment of a fee to an account that has to have a payment arrangement but doesn't have to be an authentic description of the true user. There is other information (e.g. court rules and appellate court slip opinions) which can be obtained free of charge without registration. All of these alternative approaches are legal and authorized by law in their respective situations.