I don't even know how I'd do that - even if I tried to book a flight that specifically didn't use a boeing plane in the US domestic airlines will swap out planes for different ones all the time due to maintenance requirements.
Choosing to use a competing product as an end consumer would require an immense sacrifice (like refusing to board your flight if it happened to be a Boeing, which you might get a rebate for?). Only if a significant amount of end consumers protested would the actual plane consumers (the airlines themselves) take notice - or if public opinion shifted to the point where there was a significant externality attached to purchasing a Boeing plane, but that certainly isn't the case now and I'd bet that Boeing has found some way to compensate airlines for the cost of having their planes grounded.
If airlines have to pay more in insurance premiums or they have to pay millions of US dollars a pop for each dead passenger, they'll demand a safer plane.
To my knowledge neither of these conditions have occurred in response to the 737 Max technical issues. Corporations listen to customer complaints that are backed up by losing revenue - as was shown with the issue where a passenger was beaten up on a United flight, people are extremely price sensitive when it comes to flying - there is math that can make the 737 unprofitable, but I think it's unlikely that the math will turn in that direction, it would take an extremely negative PR issue to start this.
Choosing to use a competing product as an end consumer would require an immense sacrifice (like refusing to board your flight if it happened to be a Boeing, which you might get a rebate for?). Only if a significant amount of end consumers protested would the actual plane consumers (the airlines themselves) take notice - or if public opinion shifted to the point where there was a significant externality attached to purchasing a Boeing plane, but that certainly isn't the case now and I'd bet that Boeing has found some way to compensate airlines for the cost of having their planes grounded.