Because she is a bit more mature-acting, and possibly because she is a Stage 6 boss like Eirin and Kanako (who are often portrayed as much older than the norm for the Touhou girls), some fan artists portray her as being an "old lady", or lumped into the same grouping as such. This is perhaps a bit ironic in Byakuren's case, considering how her profile states that she became a Magician to retain her youth.
Some fans did NOT take her usage of Shinki's attack pattern very well at all, most expecting Mima or Shinki to make an appearance in the Windows games after being practically forgotten about. The sight of Byakuren filling Shinki's attack stroked these fans the wrong way.
Whether it was from the attack pattern or being in Makai, some fans speculate she has a relationship or acquaintance with Shinki and is shown in artwork, sometimes suggesting that Shinki taught Byakuren some of her attacks.
She is considered something of a saint among some fans, especially when compared to the ruthless and self-centered nature of the heroines, who reject her ideals for peace. Other fans have argued that from the point of view of someone from a world where humans are oppressed, her appeals for human-youkai equality wouldn't make much sense. Others insist that Gensokyo is very close to if not exactly like her dream of a co-existence between humans and Youkai.
There's the fact that things were just a misunderstanding, and that she ends up building a temple (perhaps with helps from the heroines) afterward, which is sometimes said to be very popular with humans and Youkai alike.
Some western Touhou fans compare her to Jesus Christ because she fought for youkai but got sealed away for their sins. Because of this, fans have affectionately dubbed her "Youkai Christ" or "Youkai Jesus".