Historically, Vaishnavas and Buddhists never shied away from a strong debate with one another. Who won those debates depends on whose texts you read.
Prabhupada, also, was always ready to speak very strongly on views he felt were contrary to the truth, which, according to his estimation was the Gaudiya Vaishnava tradition of Chaitanya.
Looking critically at such texts is not offensive, as long as we do it with politeness and appreciation, for the fact that such texts benefit the followers of those systems greatly. But analysis and discernment are essential aspects of the Buddhist dialectics, a rich tradition that has led to some of the richest insights in Buddhist literature. So if we were to abandon analysis and debate for fear of offending, the dialogue would be a great deal less interesting- for both Buddhists and Vaishnavas.
I myself made an exhaustive study (as exhaustive as possible according to my limited faculties) of the Gaudiya Vaishnava tradition in middle school before choosing Buddhism, so it is a tradition that I have a soft spot for, despite it being highly polemical.
In order to ensure my mind never comes under the power of the self-cherishing attitude,
I must obtain control over my own mind.
Therefore, amongst all empowerments, the empowerment that gives me control over my mind is the best,
and I have received the most profound empowerment with this teaching.
brtsal ba'i bkhra drin