In general, briars tend towards being energetic, straightforward, and single-minded. This can mean that when they decide something is a problem, they will remove that problem by the most lateral means they have available, without consulting anyone else. This can be annoying for some people.
Briars are also associated with Freedom Heresy because of their psychological inclinations (and because historically they usually make up a signficant chunk of Freedom cults), and with the Vallorn because they’re born of spring magic.
In the Marches specifically, briars are known to corrupt the land. A buried briar causes all manner of unpredictable Spring magic to manifest in the land surrounding the corpse. As a proper Marcher burial entails being done on your steward’s farmland beneath an appletree, this tends to be what Marchers call “bad for farming”. This worrying effect has built up a lot of superstition around briars, to the point that some Marchers wouldn’t let a briar work their land for fear the sweat will corrupt it.
Briar is also the easiest lineage to hide once it’s manifested, and the most likely lineage to manifest late in life without any prior signs, which means you never know for sure the unlineaged human you’re talking to isn’t secretly a briar…
In short, briars are tied to unpredictable magic, are inconvenient to have around, provoke paranoia, and prejudice has a kind of inertia that means once it gets started, people will come up with all sorts of reasons to keep it going.