[X] Take the Ways, as Monoc Intends
OK, I'll give you Dresden. I still don't think the comparison is really transferable to us with Lara, though. The supernatural world is a much harsher place and the White Court, or at least the Raiths, are basically more like an average "law-abiding" citizens of it, not an equivalent of what a crime lord is to mundane people. That would be more like having a reputation of being friendly with Denarians and the Fomor.
For the association to have actual negative consequences for us, there would need to be a faction moral enough to care about a connection to White Court, yet flexible enough to still deal with someone who has an aura like an Infernal Exalted does.
So, that pretty much means White Council, which we are mostly avoiding anyway. For the Gray Council, McCoy would dislike it, but we already have an in through Vaderrung. The Library of Congress might be more likely to consider us a security risk, but it's not like we want to become their subordinate either.
So, it has some negatives, but I still don't think it's some big general problem that needs immediate solving for it's own sake either. Wanting to concentrate, focus and grow our power is goal for its own sake. It also invalidating some rumors would just be a nice side effect.