Rabbi Shlomo Zalman Auerbach permitted classical music during sefira.
R’ Shlomo Zalman’s opinion is recorded in Halichos Shlomo, Moadim, 11th perek, 14. See however, Orchos Halacha 54, which clarifies that this heter should only be utilized in case of need.
The overall approach of R’ Shlomo Zalman zt”l seems to be that what determines whether music is permissible during sefirah is not whether it is instumental or vocal, but rather, the type of mood attached to it. Any music, even vocal, would seem to be prohibited if it’s the type associated with dancing. (I hope this answers StuffedCabbage’s question.)
Your rov picks and chooses the psakim he likes from various poskim.
He would listen to nothing else that Rabbi Shlomo Zalman Auerbach would have to say about many other things.
Do you know his rav and all of his psakim to make such a negative comment?