It makes you allergic to all mammalian meat and potentially other products made from mammals. Outside of the allergic reaction (including anaphylaxis) I wasn't able to find any other negative effects.
oh, I just ran across this:
According to survey results presented at the American Academy of Allergy, Asthma, and Immunology's (AAAAI) Annual Meeting, some alpha-Gal Syndrome patients have a wide range of seemingly new symptoms, such as those involving the cardiovascular, nervous, and motor systems. Furthermore, some patients reported a wide range of mental health issues, such as anxiety, depression, fatigue, poor memory, irritability, sleep disturbances, etc.