There are many schools of thought like VisistAdvaita, Achintya Bheda Abheda and Dvaita which are followed by different sects of Vaishnavites. Most of these Vaishnava sects seem to be very critical of Advaita as they see it alien to their beliefs. However, I am a Vaishnava myself and attracted to Advaita Vedanta. Can I be both an Advaitin and Vaishnava?
Yes, Advaitha is too generic, you can be almost anything, when you are an Advaithi.
Besides, Adi Shankaracharya himself was a Vaishnava, he composed many stotrams on the highest Lord as Vishnu. And confusingly enough he was also a Shaktha, Shaiva etc.
Because one of the core philosophies of Advaitha is that the same ethereal Brahman underlies all existence and all forms. So yes, you can be an Advaithi and a Vaishnava.