Rude or not?

Do you not have ‘find my friends’ or similar for just this sort of situation? Maybe that would help.

My husband would always let me know when he landed and when he got to his hotel.  Also i knew the hotel where he was staying.  He usually traveled with a co-worker, so they would all go out in a small group, and drive together.  He is very safety cautious, so he was always careful when he traveled.

Why wouldn’t it be on DH for not having his keys?

Why would the house be unlocked, ever, especially when OP goes to get in the shower?

It isn’t really rude, but definitely inconsiderate because you specifically asked him to. Usually either one of us would automatically call or text the other if we were going to be getting back later at night. We live where there are a ton of deer and other wildlife out running around at night, plus drunks leaving the bar, potential health issues, etc. It’s just good common sense for someone else to have an idea of your general whereabouts when you’re out driving around alone at night or far from home.

In my house, that wouldn't be considered rude... maybe more forgetful if it had been requested. I do ask my husband where he is going if he is biking and I know about how long those trails will take. When he is out biking 30 miles on our hills/mountains I keep it in the back of my mind when I should expect him. I hear about heart attacks from very healthy people out biking a lot. For a party or hanging out with friends? I don't care at all when he'll get home. I guess I also wouldn't want to have to report when I was leaving either.

ETA: We're all so different with how we use our phones.  Some people have them attached to their hand and then others are more like me where we are winning if we remember to take our phone with us.  In OP's case, if he expects you to alert him when you move at work, then I can see why you'd expect the same from him.  That just isn't where we are as a couple, so his lack of returning the favor didn't seem rude to me. 

How does he drive his car without his keys?

I’ll validate you on this. Our house is ALWAYS totally locked up tight regardless of the time of day or night unless we’re literally right outside the door. We switched out our exterior door locks with the keypad kind that you punch a code into so our kid wouldn’t have to carry around a house key. Our garage doors also have keypads with codes. When we close the entry doors they automatically lock. The only door that doesn’t lock by itself is the patio door and we’re pretty vigilant about keeping that door always locked.

FWIW, we have a big stupid dog that lives and breathes for DH, so if DH was out late and came home unannounced, the dog would hear his vehicle from a block away and would start barking his fool head off and doesn’t stop until he’s actually inside the house, so his arrival home would definitely not be a secret, LOL.

Makes sense.😀  I still wouldn't classify him as not calling you as rude, but I can understand your being startled when he didn't let himself in. 

It was thoughtless. You asked him to do something reasonable, he didn't do it.
That would have mildly annoyed me.

The shrug? That's when some shit would go down. LOL
Unacceptable, and I would be dropping some sentences. "I noticed you shrugged when I reminded you about calling home. I feel like it was a reasonable ask, and you didn't do it, and I feel like you're being dismissive. Safety is important to me. I would appreciate it if you would show the same level of concern that I show for you."

Eh.

I ALWAYS call my DH when I’m headed home. He worries about me driving the curvy roads. If he’s an hour or more away, he’ll usually call. If it’s been a while I might text him just to check in.

I wouldn't call it rude; more like annoying. Once dh said he was going to check a field or one of the pivots or something (we farm) and wouldn't be long. If I remember right it it was just before lunch time. I called him about 2 hours later saying "where are you?". He was 35 miles away in another town getting parts. He didn't think anything of it, but yes, I was annoyed.

Our front door locks automatically (from the outside - inside not locked) when you shut it. 

And to answer the original question - I don't think it's rude, maybe inconsiderate. My DH usually messages me when he is leaving work in the evenings, especially if he is later than usual,  but it is to let me know when he'll be home for dinner. When he goes out for dinner, he gets home when he gets home. When he is travelling for work, it is rare that he lets me know what he's doing, except on the day he is coming home, and that's usually about flight delays. 
I also rarely text him about what I'm doing or when I'll be home. I did recently, but it was the second day in our new house, with totally new public transport routes, late at night. He still didn't answer his phone when I called because I couldn't open the front door to the building - turns out I was just turning the key the wrong way (new house and all that!)