I'm 5'8" and wear my hair short and pass 99% of the time. Claire is 5'3" and has overtly feminine hair and probably passes 99.9% of the time. But you sure don't forget that 1% or that 0.1% when it happens.
My point is that a statement like "there's no trans-dar" is utterly false. People point their trans-dar at me all the time, because figuring out "what I am" is a fun game to them. People do this to everyone, all the time, because categorical perception is baked into our genes, and gender policing is baked in to our culture. You can wish the world were better, but saying won't make it so.
Well I used to live in a big city here in Spain. One nice thing about this city: People don´t give a rat's a** about meeting celebrities from sports and media on the streets, in the cafe where they're having breakfast or in the queue at the supermarket. The city has a bustling GLBT scene, the second liveliest CSD in Spain and a popular gay holiday spot is nearby, so expect to meet more queer (gender- or otherwise) people than in Smalltown, Elsewhere. And you know what I always thought really nice? They give as much as they do about celebrities. I have, of course, spotted transwomen, be at the beginning of the transition, or for whatever other reason not passing too well on the underground, the bus, on the train or all around the city. And guess what? I have hardly seen a giggle, staring or strange reactions. Of course, it does happen, and once is possibly once too many, but I do think 99% of the people know how to behave and do act in a natural, unoffensive way. Now, that makes it "only" 1% left to worry about (and sooner or later they will be extinct or learn and know better). Of course in smaller, less cosmopolitan cities, the situation will be different.
I personally think Claire has little to fear from the regular QC cast. They all have shown an attitude of coolness, tolerance and non-discrimination against all possible sexual orientations and stereotypes that they will not put Claire and/or Marten in an uncomfortable situation about her transexuality, should it become known beyond Emily, Marten, Clinton, Claire's and Clintos's mom and (possibly) Tai so I expect the best intentions and behaviour from all of our regulars, really, I am very optimistic about this.