Can poor hygiene cause acne?

Yes: Acne is caused by many things (multifactorial) but one factor which can exacerbate acne is hygiene. Excess oiliness especially around the hairline (ie: sweating, long hair, using lots of hair products, etc.) can cause acne on the face, neck, shoulders, and back. Pulling the hair back, washing hair of oil and hair products before going to bed, washing immediately after working out can all help.

Yes: More commonly, acne is caused by hormonal imbalance and genetic tendencies, but poor hygiene can certainly play a role.

Usually not a cause: Acne occurs when skin glands produce more oil, but the openings of the glands are blocked by little plugs of dead skin cells (comedones). Skin oils leak sideways into the skin, causing inflammation that brings in lots of white blood cells, forming a pustule. Not washing enough usually doesn't cause acne. Causes include hormonal changes, emotional stress, certain medicines, skin rubbing, etc...

It may make worse : Poor hygiene may lead to increased pore obstruction and bacterial growth which can exacerbate acne although it may not necessarily cause it.