The evidence in Vācaspati-miśra’s works suggests that he must have had Śaiva leanings. Cf. p. of my 2001 article “The prologue and epilogue verses of Vācaspati-miśra-I." Rivista degli Studi Orientali 73: 105-130.

Since the journal in which the article was published may not be easily accessible and since the article contains many other observations relevant to the history of Advaita Vedānta, Nyāya, etc., I attach a copy of it here.