I think you’re misunderstanding the problem. We already have vaccines that cause positives on antibody tests. This is quite common. For example, the HepB vaccine causes positives on the HBsAb test, and people who administer the test understand this.

If we had a widely available vaccine and effective vaccine for HIV that affected certain tests, this would easily be justified by the benefit of the vaccine in preventing HIV. And the results of the antibody tests could potentially still be used to assess HIV immunity.

But a COVID vaccine that caused HIV tests to report positive without conferring any immunity would be bad — the test would essentially become useless. Re-engineering the vaccine to avoid this seems like a no-brainer.