Well I sort of wrote a thing regarding Naruto, Sasuke, and Shikamaru reacting to Shikako dating (or at least, the idea of her secretly dating someone) in Don’t Hold Back… But I guess since they were mostly blindsided by the secrecy, it’s a different situation entirely…
Hm… Kakashi would be fairly hands off (though quietly menacing in the background) whereas with Naruto and Sasuke it would depend an awful lot on who exactly Shikako is dating. Naruto would get over it quicker, so long as everyone involved is happy, though if it were someone like, say, Kiba he’d probably loudly argumentative–”Really? Dog Breath?”
Sasuke would. Well, I headcanon that Sasuke has very mixed feelings about Shikako. Like obviously, he loves her, but even he’s unsure if that’s platonic or romantic love. So at first brush, he’d probably be mildly jealous regardless of who Shikako is dating, and only slowly let it go once he comes to terms with his feelings for her and once Shikako’s significant other proves themselves as “worthy” of dating her. Like, for example, if it were Gaara–”But is he strong enough?” “Sasuke, he is literally the Kazekage.” “So?”
Shikamaru, given his continued overprotectiveness and attempts to manipulate Shikako into being safe, would probably mess with Shikako’s significant other so badly. Just like, constant head games and Shikamaru bribing Academy students to annoy the shit out of them… that sort of thing. Because if they can’t handle small obstacles in their daily life, there’s no way that Shikamaru is going to give his approval. He probably pulls the “future clan head” card at least once as well as the “what are your intentions towards my sister?” Basically, Shikaku and Yoshino don’t really have to do anything because Shikamaru’s got the vetting process down to an art form.
Shikako, of course, is not impressed with any of this. It’s so unfair! No one put TenTen through all this when she started dating Shikamaru!
To which TenTen replies–”Really? You think Ino didn’t put me through a gauntlet?”
Hahaha, I dunno. Something like that, I guess.