The scenario Jim imagines is called the "chicken dilemma", because it resembles a game of chicken between the Green and Democratic voters. If one group is more cooperative, they lose by a little; but if both are uncooperative, they lose by a lot. It is not impossible, but opposing approval voting because of it is like driving cross-country on a motorcycle because you think airplanes are too dangerous. That is to say:
1. This basic situation would be rare. Generally, there will be two candidates who stand out as stronger than the others. A leftist district like the one you describe, with strong Green and Democratic factions, would often have fewer than 1/3 Republicans, in which case there is no danger of this.
2. If this looked as if it might happen, people would see the possibility, and there's several ways to avoid the problem. If the Green really only has 39% solid support, the Democrat would probably argue that they are actually the Condorcet winner, and try to demonstrate secondary support from Republican-leaning independents in order solidify their position and encourage Green voters to be cooperative. Of course, if the problem is that it's a Democratic incumbent seen as corrupt by most, the Green could do the same thing. In both cases, this "broad appeal" strategy would probably prevent a chicken problem.
Remember, we're comparing this to Plurality. A "chicken dilemma" problem would be rarer than spoilers in Plurality, because it requires more specific circumstances, and is more avoidable even when those circumstances threaten. Certainly for a Green, who under plurality is accused of being a spoiler in every single election, this is the kind of problem you'd love to have.
If you want a voting system that deals well with the chicken dilemma, there are such. SODA or "improved Condorcet" systems do very well; and median systems (ie, Majority Judgment, etc.) would let voters put their second choice near but not at the bottom, which would work well (both individually and societally) in this scenario.
Finally: it seems that Mueller is comparing Approval to PR. Of course, these are not antithetical ideas; most of us here would enthusiastically support bills or initiatives for either one of these.