You're right about both - their marketing is really on point. But allow me to propose a few additional reasons for Target's popularity among suburban liberals:

1. Prices are slightly higher that Walmart, which keeps away the most budget conscious shoppers (ie, couponers & low-income people will go to walmart to stretch their money). Because lower-class shoppers are less visible at Target, middle-class shoppers flock to it, and even non-middle class people who can swing it may prefer it because it confers higher social status. (This is also why the common nickname for Target is "Tar - Jhey", aka, "Target" with a fake french accent to mock the aspirational bougieness of the brand).

2. Target has fairly aggressive policies about how long customers should have to wait in line (if there's more than 3 people waiting, the manager is supposed to call a sales floor person up to assist) + a policy on how long checkouts should take to complete (they actually give the cashier a pass/fail score that everyone can see after each checkout, and if the average is too low, it's grounds for dismissal). For the customer, this does mean a faster checkout. For the employees - it means more work interruptions and ultimately more work to do at closing.

3. Target doesn't even attempt to provide certain products and services that are culturally associated with rural/poor America. They don't sell guns, they don't cash checks, they don't have gardening centers.