Supergirl has always had pretty lax standards when it comes to how Kara protects her secret identity. On Earth-38, all she really needs to get by is a pair of glasses and a pulled-back hairdo to convince everybody around her that she's totally a regular human and not at all a Kryptonian superhero. Soon, however, she'll take a big risk as Supergirl that could reveal her secret identity to somebody who would probably like nothing more than to share it with the world: CatCo editor-in-chief Snapper Carr.
An upcoming episode will feature Kara and Alex as they realize that they'll need to cross some major lines if they want a win in their fight against Cadmus, and one of those lines will involve Kara's secret identity. In a desperate attempt to convince her boss to run a story that would assist in taking down Cadmus, Kara agrees to set up an interview between Snapper Carr and Supergirl. It won't be the first time that she's chatted to somebody she knows as Supergirl, but it might be the riskiest.
Cat Grant came close to discovering Kara's secret throughout Season 1, and Kara had to resort to some pretty extreme means to avoid discovery. Still, Cat came to count Supergirl as a friend, and she really didn't want to expose Supergirl. If anything, Cat was one of Supergirl's biggest protectors. The same can't be said for Snapper Carr, who is more objective about the Girl of Steel and less inclined to avoid the truth if it gets in the way of a good story. If he gets close enough to Supergirl to take a good look at her, he could easily realize that she bears a striking similarity to Kara. She certainly demands plenty of his attention as his employee, and he's an observant man.
Of course, Supergirl does take place in a world in which both Superman and Supergirl can fly around in broad daylight and make the nightly news without anybody connecting the dots to their secret identities, so Kara might not consider her chat with Snapper to be especially dangerous. That said, Season 2 has already introduced one character who was able to figure out that Kara and Supergirl are one and the same. Maggie Sawyer simply pointed out that the glasses don't really do all that much to obscure Supergirl's identity, and while the scene was played for laughs, it did set a precedent for characters seeing past the spectacles and realizing that Kara is Supergirl.
It should be interesting to see what Cadmus does in the coming weeks to motivate Kara to agree to the interview with Snapper. Lillian Luthor escaped the authorities in the latest episode, and we can bet that she'll be back pulling the strings at Cadmus sooner rather than later. Throw in the fact that the Danvers sisters still need to figure out the mystery of Jeremiah's captivity with Cadmus, and the stakes will be awfully high for the Kara moving forward.