You said that budgetpost is alphanumeric. That means it is looking for comparisons against strings. You should try enclosing your parameters in single quotes (and you are missing the final THEN in the Case expression).
UPDATE tab1
SET budgpost_gr1= CASE
WHEN (budgpost in ('1001','1012','50055')) THEN 'BP_GR_A'
WHEN (budgpost in ('5','10','98','0')) THEN 'BP_GR_B'
WHEN (budgpost in ('11','876','7976','67465')) THEN 'What?'
ELSE 'Missing'
END