Any code authored by or for (exclusively) the government is default open. Usually all it takes is a FOIA request; if you're lucky they're publishing it on github already. However there are carve-outs for areas where making the code public could impede the law-enforcement mission of the entity that uses it, that is, FOIA exemption 7E. Since the IRS knows that if you knew how the audit worked*, then you'd do your taxes "just so" to avoid the thresholds by running the logic yourself, which is not something they'd want to encourage. And it would definitely increase their audit casework load.
There's also the issue that if the code wasn't bespoke but also sold to non-government entities for similar missions (i.e. government does not hold exclusive rights), then it can be protected as the contractors IP. But for the IRS this would be rare, they are pretty unique and often do things their own way.
* You can sort of do this without the code. The IRS is not allowed by legislation to base an audit decision on any information that is not covered by eFile, so contents of forms 1041QFT and 990T, or any attachments to what could have been an electronically submitted form, is out of scope. As long as what you submit in the core set of forms aren't statistical outliers, then you're good.
There's also the issue that if the code wasn't bespoke but also sold to non-government entities for similar missions (i.e. government does not hold exclusive rights), then it can be protected as the contractors IP. But for the IRS this would be rare, they are pretty unique and often do things their own way.
* You can sort of do this without the code. The IRS is not allowed by legislation to base an audit decision on any information that is not covered by eFile, so contents of forms 1041QFT and 990T, or any attachments to what could have been an electronically submitted form, is out of scope. As long as what you submit in the core set of forms aren't statistical outliers, then you're good.