Alexis Rose is my favourite representation of an avoidant attachment style because on the surface she is the most sociable Rose and she does consistently pursue relationships and this is a pretty good deflection from the fact all of these relationships are superficial. All of the other Roses develop a connection to a shifts creek citizen (Stevie and David, Jocelyn and Moira, even Roland and Johnny although that’s far more contentious), but Alexis’ only interactions are romantic.
This comes up a couple of times in the first two seasons, once when she tried to invite Twyla over and is rebuffed both by David (saying she’s never had a conversation with Twyla outside of her work) and Twyla herself advising Alexis to practice being alone and reminding her of the fact she dated Twyla’s ex after advising them to break up. Alexis, despite being the most extroverted Rose, has no friends in early seasons and doesn’t seem to have any substantial contact with her friends from before they moved either, although unlike David she never expresses any disappointment about this. This implies Alexis’ approach to friendships leans towards friendly acquaintances, lacking intimacy and loyalty but freeing her from any emotional depth.
Her avoidance comes up more clearly in relationships. Ted in early seasons is the obvious one, she almost begins sabotaging the relationship immediately when she realises Ted is emotionally invested by pursuing Mutt. Once she has Mutt the relationship is completely hollow, something they discuss when they break up. Alexis’ pre-move relationships seem to fall into this hollow surface level attraction category, mutually in the case of Stavos (her boyfriend in the first episode). I think there is definitely an argument to be made that Mutt and Alexis’ break up wasn’t hard for her because of Mutt specifically but because the relationship ended over a lack of emotional depth, something Alexis has previously avoided and now has to acknowledge she actually wants. Thus her immediate pivot back to Ted, he can give her this and has previously been willing to do so giving Alexis emotional intimacy without expecting reciprocation. However, Ted has changed and because of the long pause in their relationship Alexis has time to learn and reciprocate the vulnerability Ted gives emotionally and by the end of the show Ted and Alexis has an incredibly healthy relationship.
Alexis is also quite avoidant when it comes to her parents as well. She doesn’t expect anything from them when it comes to support (she is surprised in season 2 when her mother buys her cold medicine, stating she has never done it before). Johnny and Alexis seem to be the stronger of her parental relationships but even that at the beginning of the show is incredibly distant. In fact the only family member Alexis consistently asks for things from is David. The person she most relies on for conversation is David too, and yet at the end of season 1 when David proposes moving in together she balks at the idea. David is often the only one aware of Alexis’ past dangerous escapades, even featuring once or twice and at the beginning of the series he is the person Alexis cares most about but he is still held at a distance.
Most of this can be rooted to the fact that universally liked Alexis doesn’t believe people can both know her and love her at the same time. As the series progresses we see more of Alexis opening herself up to this possibility and being more vulnerable, which is ultimately the changing factor in Alexis’ and Ted’s relationship. It’s not just that she’s changed, although she has improved, it’s that she’s capable of investing herself in relationships because she believes they can be emotionally open without her being rejected.
(Also side note I did love Ted’s comment to Johnny after the failed proposal. “And it's rare to find someone that beautiful, and smart, and deeply selfish, yet charming.”, because it shows he did know Alexis and loved her anyway, even though she seemed to believe he was blind or unaware of her worst qualities.)
