If Boston gets Butler and has room for Hayward I think that greatly lowers our chances of keeping him. The only thing we would have going for us is that Hayward probably doesnt want to be 4th fiddle and probably does not want to play with IT. But he might sacrifice that to be on a team that might push Cavs and GS.
The other thing that might be going for us is that Blake Griffin would probably be a better fit for that team. Especially if they keep Crowder and Jaylen Brown. Those two can hold down the SF spot pretty well. I think a IT, Butler, Crowder, Griffin and Horford is better than IT, Butler, Hayward, Amir or Jerebko and Horford lineup.
If Boston wants Butler and Chicago does want to trade him they will get him. No one can outbid Boston for Butler. I guess I am assuming Chicago is going for a rebuild and not a reload although Boston could offer them parts to do both at the same time. Cavs, Jazz and others cant really offer much except veteran players and late draft picks that are not worth rebuilding with.
Utah could easily counter Boston getting Butler if they get their own player of that quality like PG13, or maybe a couple players like both PG13 or Love and Bledsoe or Lillard. I know some of that might not be possible but Jazz should be very active looking at any all-star level player and making offers and being very aggressive.