He voted for a vaccine database. His argument in the tweet is that he did it for your own good by making sure there were "restrictions" before others made a bill without one.
He absolutely voted for the 2021 NDAA bill with RFL's in them. It was only stripped in the Senate version before it was signed into law.
Further, Crenshaw defended RFL's in his Joe Rogan interview. He's only backpedaling now because of how unpopular they are.
H.R.550 - "IMMUNIZATION INFORMATION SYSTEM DATA MODERNIZATION AND EXPANSION
"In this section, the term ‘immunization information system’ means a confidential, population-based, computerized database that records immunization doses administered by any health care provider to persons within the geographic area covered by that database."