I'm asking you what your concern is regarding Wasabi since Wasabi is specifically designed to defeat chain analysis businesses by coinjoining your BTC with other users, making it impossible for chain analysis businesses to trace inputs to outputs.
If it's specially designed to defeat chain analysis businesses, why does zkSNACKs, which is the repository owner, cooperate with them and say they're likely to treat some outputs differently than others[1]?
No, the software does not deny outputs. Your keys, your coins.
The software per se will not deny spending certain outputs, but the default coordinator (which I'm reminding you is hosted by the founder of this project) is not going to accept certain outputs from being mixed, according to their announcement.
Nothing happens if anyone calls your coins "dirty".
Apparently, it does happen. You're not allowed to mix them on the coordinator with the highest volume.
[1]
https://twitter.com/wasabiwallet/status/1503091503207432193