Your question is a complicated one, because you ask both about behaviors (of which there are few) and the citizens of Starkfield, who are stereotypical, close-mouthed New Englanders. These two factors in Ethan Frome make it difficult to determine how much of their reticence to speak of either Zeena or Ethan is protectiveness and how much is simply their natural disinclination to be talkative.
Clearly the narrator is a newcomer in town, here to do a temporary engineering job. At the post office, he gets a bit of Ethan's story. He learns that the only mail they generally get is the newspaper or mysterious packages from odd patent medicine companies. He learns there has been a "smash-up" which has left Ethan not only incredibly scarred from head to toe but has also left him looking like "a man who was dead and in hell now." He learns that Fromes live a long time (perhaps even if they shouldn't or when they don't particularly want to). He learns that Ethan had to stay in Starkfield to be a caretaker--first for his father, then his mother, and now his wife. The town native, Harmon Gow, says:
“Guess he's been in Starkfield too many winters. Most of the smart ones get away.”
That's a good start on Ethan's story. The narrator's landlady adds a few more details: Ruth Varnum saw them first, it was a tragic event, and it happened down at the bend of Corbury Road. After that, no more. The narrator said:
on the subject of Ethan Frome I found her unexpectedly reticent. There was no hint of disapproval in her reserve; I merely felt in her an insurmountable reluctance to speak of him or his affairs, a low “Yes, I knew them both…it was awful…” seeming to be the utmost concession that her distress could make to my curiosity.
That's actually quite a lot of information from this very tight-lipped community. Harmon Gow is clearly sympathetic to Ethan's plight, and the landlady appears to be unwilling to speak any more of Ethan's woes. If she's protecting anyone, it's Ethan. It appears more, though, that the episode (the "smash-up") simply makes her inexpressibly sad.
I'm gathering you haven't read beyond chapter one, so I want to be careful about how much I reveal here; but it seems that any reluctance Harmon has to speak of the event comes from his natural disinclination not to speak too much to strangers, and the landlady's hesitancy to speak comes from her unwillingness to talk about painful subjects. Neither appears to simply distrust foreigners and refuse to talk to our narrator.
In the story Ethan Frome the attitude of the people of Starkfield are representative of the typical people who live in isolated villages where everyone knows each other, as well as each other's business. They actually are very self-contained and tend to get ill a lot due to the bad weather at Starkfield. Like in many other small towns, they are pretty much into doing their own thing their own way.
After Ethan's accident, the townspeople seemed to be in a bit of shame for Ethan's sake. This being said, they may have slightly sympathized with Zeena, especially after they saw how she ended up taking care of Ethan and her cousin.