How compelling is the distinction between the first- and the third-person perspectives as an argument against naturalism?

Naturalism commends the use of the scientific method for studying mental processes. But many philosophers claim that these are first-person phenomena, only accessible to the subject performing them. Sciences, however, would require empirical and intersubjective verification (third-person perspective). So, can conscious states be studied from the scientific perspective? If not, is that not possible ‘today’ or is it completely impossible? Would that imply that it is necessary to abandon naturalism? Should naturalism be extended in order to make room for mental phenomena?