As all the others already mentioned the Loop is working for me. I am wondering why you are using a WHILE LOOP in the first place, but let's not question this for now.
I created the following minimal example. Let's assume your data looks similar, then your results would return nothing because of Boekdatum is not smaller than StartDate for each Loop, but equals StartDate. Therefore in the line AND Boekdatum <= @Startdate I replaced = with <= and I removed (nolock). Maybe this will resolve your "not working" LOOP.
DECLARE @FC_GBRMUT table (Rapportagedatum date, Boekdatum date , Rekeningnr int , Bedrag varchar(100), Uw_referentie varchar(100))
INSERT INTO @FC_GBRMUT
SELECT '20200101', '20200101', 14050, 'RandomText', 'RandomText'
UNION SELECT '20200201', '20200201', 14050, 'RandomText', 'RandomText'
UNION SELECT '20200301', '20200301', 14050, 'RandomText', 'RandomText'
UNION SELECT '20200401', '20200401', 14050, 'RandomText', 'RandomText'
UNION SELECT '20200501', '20200501', 14050, 'RandomText', 'RandomText'
UNION SELECT '20200601', '20200601', 14050, 'RandomText', 'RandomText'
UNION SELECT '20200701', '20200701', 14050, 'RandomText', 'RandomText'
UNION SELECT '20200801', '20200801', 14050, 'RandomText', 'RandomText'
UNION SELECT '20200901', '20200901', 14050, 'RandomText', 'RandomText'
UNION SELECT '20201001', '20201001', 14050, 'RandomText', 'RandomText'
UNION SELECT '20201101', '20201101', 14050, 'RandomText', 'RandomText'
UNION SELECT '20201201', '20201201', 14050, 'RandomText', 'RandomText'
DECLARE @Startdate DATE = '20200101';
DECLARE @Enddate DATE = '20210101';
WHILE (@Startdate < @Enddate)
BEGIN
SELECT Rapportagedatum, Boekdatum, Rekeningnr, Bedrag, Uw_referentie
FROM @FC_GBRMUT --(nolock)
WHERE RekeningNr =14050
AND Month(Rapportagedatum) = MONTH(@Startdate) AND Year(Rapportagedatum) = YEAR(@Startdate)
AND Boekdatum <= @Startdate
SET @Startdate = DATEADD(m,1,@Startdate)
END
WHILE (@Startdate < @Enddate) BEGIN SELECT @Startdate SET @Startdate = DATEADD(m,1,@Startdate) ENDyou should get 12 dates.WHILEloop and what do you want to achieve ?nolock?