These boundary-challenged guys just seem to have trouble in all areas of their lives, don't they? My SO is like that, too. Many chicks he's worked with or lifted weights next to at the gym act like my SO is their best guy friend in the whole world, and say and text things that seem just a little too familiar. Things most people wouldn't feel comfortable saying to an acquaintance, but it must be the lack of boundaries that fosters that sense of "I can tell him anything!" But they don't realize that he is that way with everyone. You know that feeling when you first meet someone of an instant, intense connection? It's not that you are soul mates. It's lack of normal boundaries. 

Is whatever it is that keeps you from leaving him really that bad? The man does not treat you well, in any part of your life together. You deserve so much better...

Appropriate or Inappropriate?
 

If you have to ask, then you already know the answer 

Especially if he got mad at you for his same exact behavior. 

he needs to block her...not respond and encourage her.  Oy....why o why can they not figure out.  I have to keep illustrating to H...."if I did x y z....how would you feel? "  If the answer is o h3ll NO in regards to me...THEN ITS O H3LL no for you too.  

I mean really what he is getting out of it..other than an ego hit cause someone is texting him.  

smh..the double standards are exhausting.

I really hope his good quality are better then his bad qualities,  you have your hands full.  You know the answer, there's something going on. At least in Chefs mind.  This woman must have a lot of time on her hands ..,  You can start by telling him you don't approve of this type of "friendship"   You must also stop this type of interactions if you are even having it .  BUT we are here for the vent 

my rule of thumb (in the past not w/ my Mr now) was simple: if you'd do/say/share it in front of my face, it's okay but if you would never be that familiar/flirty/sharing in front of my face then you know it ain't right. 

DH has told me (not me snooping) that an ex contacted him on social media. Also from like 15 years ago. He was upfront and just said "_____ messaged me. Just wanted to let you know. She asked about ________ and how ________ was going. I did respond and left it at that." They aren't in contact regularly and he may hear from her every 5ish years? So I wasn't worried. Especially since he wasn't trying to hide it. 

I don't think that's the same at all for your case though. 1. He's hiding it 2. It's already been a problem in the past. He 100% knows what he is doing is inappropriate, bothers you, and it continuing to do it anyways. 

No, thats very inappropriate.

Ive had issues with husband and women that I know and have introduced him to, lacking boundaries or not respecting boundaries. Its a no-go-zone for me. Husband broke it off with Toxic Troll for her online shenanigans...

This is a question that someone being gaslighted asks. You know what the answer is, you don't need to post here for validation.   

I am in camp ... So what?  If he is a man of character, this is a non issue.  If not, you picked the wrong partner and need to boot his ass out of your life.  As this is repeat behavior, the facts point at the second result.

Black, meet white. No grey.  Particularly on this topic.

My XW had a dating problem our entire engagement and marriage.  As we were divorcing she on multiple occassions commented "We can date you know."  Ummm nope. My response  was always along the lines of "I have been married to you. What makes you think I would want to date you?"  

Just the thought of  "one more hook up" with that skank whore makes my skin crawl. Dating her would make me peel my own skin off.  Oddly, this is not an unusual thing to occur in divorcing or divorced couple sitatuations.  One last romp.

Chefs periodically sniffing this trolling skank's ass is not something I would tolerate if I were you. So, don't tolerate Chef.

That said. I do have a very close old friend who I speak with periodically.  DW and I have been to their home for celebrations a number of times over the years. She is also a former lover. We don't speak much these days but occassionally she will call or I will call to check in.  She was there during my first marriage and was very supportive during the end of it.  She lost her dad around that same time.  We were each others support.    After my divorce, we became intimate.   

DW loves her to death. She talks more about my DW when we speak than she does about herself or her family.  So do I. They both enjoy giving me shit way too much.  This is one of those "You know it is a problem when it is a problem." things IMHO.  It is either okay and appropriate, or it isn't.

This does not pass your smell test. That, is what matters.

Take care of you.

If it bothers you (and it would bother me) then it's inappropriate. Ask him why her feelings(responding to her texts) are more important to him than how you feel? 

That being said, I don't think Chef has any intentions on taking things further, but he probably enjoys the ego boost and you're not wrong to tell him to shut it down. 
 

ETA Reading the comments, I hate to see how many women have to put up with this sort of thing (including me).You're not alone. 

Inappropriate

If you have access to the cell phone account you can simply deactivate his and put him on house phone (and non smart flip phone for super elderly people where they can only access people who are in their contacts) 

"Accidentally" knock his phone in the toilet or put some coconut oil on your hands and let it ever so gently slide down a cliff/out a window/etc  

You said he's not tech savvy and he never saves people's numbers. 
 

*now I'm not married so take this with a grain of salt but a man who is supposed to be my life partner acting unsavory = p*ssy protest
 

Let him scramble. 

She has already sent him inappropriate messages ? I'd be done at that.

And it's not a double standard if you are able to maintain platonic  friendships with members of the opposite sex ,and he can't.