most likely you want to use brackets there
condition1 and condition2 or condition3
is true when only condition3 is true
condition1 and (condition2 or condition3)
is true only when condition1 and one of the following two is true
in your SQL code you are missing ELSE part
i think your case should look like that:
SELECT
CASE WHEN .Sequence = 0
AND (
Category = 'Diphtheria, Tetanus, Pertussis' OR
ImmunCode = '90696' OR
ImmunCode = '90723' OR
ImmunCode = '90698'
)
THEN #temp.ImmunDte
ELSE
END AS DTPInjectionDate1
FROM #temp