Disclaimer, I have no context about FIRE. But, I feel there are a few possible reasons for this:
If the culture on a college campus has little-to-no bias towards sharing or suppressing conservative ideas, them singling out conservative ideas being suppressed would give you enough of a signal that they are conservative leaning.
If the culture on a college campus biases towards sharing conservative ideas, them singling out conservative ideas being suppressed would give you enough of a signal that they are conservative leaning.
If the culture on a college campus biases towards suppressing conservative ideas, them singling out conservative ideas being suppressed wouldn't generate enough of a signal to justify calling them conservative leaning.
TL;DR: whether or not you consider their stance as conservative leaning will be strongly influenced by how you perceive discourse on a college campus.
If the culture on a college campus has little-to-no bias towards sharing or suppressing conservative ideas, them singling out conservative ideas being suppressed would give you enough of a signal that they are conservative leaning.
If the culture on a college campus biases towards sharing conservative ideas, them singling out conservative ideas being suppressed would give you enough of a signal that they are conservative leaning.
If the culture on a college campus biases towards suppressing conservative ideas, them singling out conservative ideas being suppressed wouldn't generate enough of a signal to justify calling them conservative leaning.
TL;DR: whether or not you consider their stance as conservative leaning will be strongly influenced by how you perceive discourse on a college campus.