My experience has been entirely positive, aside from the occasional rabid anti-Westerner (not just the rite, but all things Western). Most non-Netodox Orthodox I meet think it's awesome. Orthodoxy is Orthodoxy, regardless of rite.
It can be difficult, though, I suppose if your interactions are largely with converts. Pop-Orthodox literature that seems to persuade many interested folks into exploring Orthodoxy are largely written from a "How is Orthodoxy different than everything else?" perspective, so what entices converts is how the liturgy is described ("It's so mysterious!"), all of the symbolism, the historical roots, etc. The whole pitch is "Not the West!" How many convert podcasts, blogs, books, etc. are "The Journey from West to East" or something similar? Someone in the West who has been shaped by Western tradition and experience almost feels like they are discovering Christianity for the very first time, because things are described in such different language.
So I can see how someone in that context might feel like an outsider when all of these "new" things are still fascinating to converts and are what make up a great deal of their Christian identity. It's like being at a party with a bunch of people who just moved from your town to this "amazing" new place that they never want to leave. But, people convert for different reasons, and for some people the Eastern Rite is precisely what they need. For others it isn't. Thankfully both are available.