Likert Data: What to Use, Parametric or Non-Parametric?

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Using Likert Type Data in Social Science Research: Confusion, Issues and Challenges (2016, background): “Additionally, Pell (2005) as cited in Murray (2013) agrees that parametric tests can be conducted on the summed scores of Likert scale data provided that the assumptions are clearly stated and the data is of the appropriate size and shape.”
CLIL students' perceptions of their language learning process: delving into self-perceived improvement and instructional preferences (2016, methodology): “Although there is controversy about the use of parametric tests on Likert scale results, authors such as Norman (2010) and Murray (2013) conclude that parametric and non-parametric tests conducted on Likert scale data do not affect conclusions drawn from the results.”