Okay, anon, first things first.
“Now we’re supposed to write strong female characters,”: that should always have been the case, it has always been the case in good literature/media, and here is why.
I’m not going to go into the general problems about the portrayal of women in the media, but one general problem is having women as victims for either a) shock value, or b) having the man save them.
That doesn’t mean female characters shouldn’t have softer moments.
“Strong female character” is not the “strong independent woman” trope. A strong female character doesn’t mean she goes around punching people and hating men and not being called babe and hating all penises because men are evil.
A strong female character is one who is strongly written, aka has her own thought/motivations/reactions that are neither there to validate some other man (or even woman) or just there to move the plot. A strong female character isn’t a prop. A strong female character is written with just as much care as a male character is.
So, put it this way: would a male character seem weak if he had a tender moment with his wife? No, that’s what we call “character development.” Would a male character be lesser if he had flaws/moments of weakness/emotional fragility? No, that would make the character compelling.
If you want an example of a strong female character, just take a look at Jessica Jones. Yes, she has superpowers, and punches people, but during the entire show, those things are not what define her.
Jessica Jones is a smartass ; she will stand up against several men during the show, and her main villain is almost a textbook case of the kind of entitlement found in male abusers.
But Jessica Jones is traumatized ; Jessica Jones has panic attacks ; Jessica’s plans are often not well thought out ; Jessica sometime gives in to her lesser urges. Jessica has tender/vulnerable moments with several people on the show.
For another example: Molly Hooper, who doesn’t go around punching people, fighting crime, is generally soft spoken. She starts out very meek because of a crush on Sherlock, grows more of a backbone during the course of the show. She still stays rather soft spoken and soft hearted. Molly Hooper is a strong female character.
So, to finally directly answer your question: don’t make a difference between a male and female characters. A character is a character, and tender moments are what gives them depth.