Phthalates refers to a wide range of substances that are very different from one another. Some are considered safe, and others are considered to pose a potential risk. Those that are considered to be potential risks are not approved for use in consumer packaging were banned in the US as well as the EU (these are phthalates DEHP, DBP, DIBP and BBP). Just to be clear, these have never been used in personal care products to begin with, rather they are used for industrial products.
However, those phthalates that have proven to be safe are not banned in the US or EU (DEP, for example, AKA diethyl phthalate is used in the EU in packaging for personal care products and other consumer items, and was given broad approval of safety in 2007.
The EU (Scientific Committee on Consumer Products) did a thorough and detailed degree of research of prior and new research and found that there was no plausible risk from what trace amounts exist in packaging for personal care products.
An earlier study in 2001 in the journal Food and Chemical Toxicology already arrived at this conclusion so far as the risk of DEP in personal care products.
What is often cited as a risk by crusaders is either phthalates that are not present in personal care, food or medical device packaging materials (therefore not applicable) or studies that utilize massive doses of a type of types of phthalates (beyond what would be possible in humans).
Bisphenol A (BPA) is sometimes confused with phthalates, but is a completely unrelated substance. Either way, BPA also has been demonstrated, exhaustively, to be safe for use in packaging for food or cosmetics. In 2007, the EU found them safe. In 2009, a study published in Critical Reviews in Toxicology found that BPA poses no risk from to humans. In 2010, 2012, 2013 and 2014, the FDA found (repeatedly) that BPA is safe as used in packaging for food and cosmetics.
References for this information:
U.S. Food and Drug Administration. Bisphenol A (BPA): Use in Food Contact Application [Internet]. 2014 [cited 2016 Jan].
Critical Reviews in Toxicology, 2009, issue 1, pages 1-75
European Commission Directorate General for Health and Consumers. Opinion on Phthalates in Cosmetic Products. [Internet]. 2007 [cited 2016 Jan].
European Food Safety Authority. Opinion of the Scientific Panel on food additives, flavourings, processing aids and materials in contact with food (AFC) related to 2,2-BIS(4-HYDROXYPHENYL)PROPANE. [Internet]. 2007 [cited 2016 Jan]. Available from: http://www.efsa.europa.eu/en/efsajournal/pub/428
Food and Chemical Toxicology, February 2001, issue 2, pages 97-108