Are private listings for the sale of various items published on websites such as craigslist offers like in the Lefkowitz versus Great Minneapolis Surplus Store case, or would they be considered “invitations to offer”? Would it depend on how the listing is worded?

In my opinion, if it is listed as an offer in writing, it is valid and could be upheld in a court of law. There is no stated rule in the Lefkowitz case claiming that the fur coats were to be sold for women only, and Lefkowitz could have easily sent in a woman from the street with his $1 bill to purchase the coats.
The defendant's claim that the advertisement was "unilateral offer" which it had the right to withdraw does not seem at all valid. In modern times, if you were to meet with someone from Craigslist who had advertised a product for a specific price, you would demand that price since it was explicitly offered and agreed upon. Now, if you agree to haggle and discuss the price, that is it's own issue, but that is typically engaged by the purchaser who desires an even better price for the item.
To summarize—if it was offered in writing and explicitly stated for a certain price, that is an "offer," not an "invitation to offer." The only way wording can change that is if the seller initiates a bidding war, or if there are stipulations attached to said offer.