I think your suggestion that Elinor is worried about their social status is the most convincing. There's a fine line for these young unmarried women between being realistic and being snobbish...

I see the Jennings-Middleton-Palmer social circle as poised on a fault line between elegant and vulgar, "well-bred" and "ill-bred". Thanks to the money her husband earned, Mrs Jennings has pushed her daughters up out of the "lower" level they were born into, and they both seem secure at their new level. (Lady Middleton got a title; Charlotte will be the wife of an MP.)

But Mrs Jennings herself is still a vulgar person - she still associates with her old "low" friends and she can't be trusted to "act classy" at more elegant gatherings. Sir John and Mr. Palmer were willing to overlook those factors in order to claim the Jennings girls' dowries and personal charms. But there's no guarantee that other wealthy men would overlook them to court the Dashwood girls, who have charms but no dowries.