Did you also acount for the "mortar bed" and/or wire mesh that should be roughly 1/2" thick between the hardibacker and tile? Or is that not present?

Im not a framer but I've picked up things along the way. more often than not, as long you're not removing more than 30% of a 2x4 depth, it shouldnt compromise the structural integrity, unless there are 3 or more sandwhiched together. Those are probably directly carrying the load of whats above them.

Even with brand new houses ive seen things shaved down notched out. Especially in remodeling jobs.