The transgender censor seems to be simple string matching (if query == "transgender"). Just putting the forbidden word in quotation marks makes it searchable, too [1].
I wonder if the filter was intentionally implemented in a shitty way by NIH staff so that they formally comply with an internal order but offer easy ways to circumvent it.
I appreciate your attempt to clarify here, but your citation link above in 2) is for 'trangender', a misspelling (but it does search successfully).
This isn't a 'search problem'; searching for 'gender' and 'transgender' always and immediately redirects back to the main page. I also tested several unrelated searches without any issues (HIV, genome, public, potato).
Also, I just searched for "transgender" on nih.gov, and got lots of hits [2], the first one being a publication on PubMed [3].
[1] https://www.reddit.com/r/NIH/comments/1j28ytk/comment/mfs14d...
[2] https://search.nih.gov/search?utf8=%E2%9C%93&affiliate=nih&q...
[3] https://pubmed.ncbi.nlm.nih.gov/34993517/