Back in the days when I sat behind a sales desk I must have issued 100s of IATA tickets to people who neither knew nor cared which airline they were booked on, let alone which aircraft. They knew the itinerary they wanted, and we sorted out the ticketing, fares and reservations to get them the cheapest overall cost for that. On a long itinerary several airlines might be used.
But the internet, and development of the locos and short-haul point to point return trips, has changed all that. However, apart from a possible reaction to massive adverse publicity for a particular aircraft, it seems to me that the public's normal assumption is still that "if it's allowed to fly it must be safe", contrary to all the evidence. And then they go for the best price.
The jury's out on whether passengers will specifically avoid booking on the B737 MAX if and when it returns to service, by positively checking with the airline/agent/website operator which aircraft they are booking on and not proceeding if it's a B737 MAX. But I'll predict that the assumption "if it's allowed to fly....etc" will prevail, not least because finding out in advance which type will operate your flight is well-nigh impossible, unless the airline only operates one model variant. This is equally true of customers booking through a tour operator.