It all comes down to cost. With Abbot saying that they would likely side with the employee on an unemployment claim for termination after vax refusal, the ultimate question is what would cost them more money? Paying unemployment benefits or paying the OSHA mandate fines. Seeing as how the OSHA mandate was stayed in court and subsequently dropped by OSHA since it cannot be enforced, I imagine the least risky option for Halliburton at this point is to also drop the mandate.
The other variable at play here is customer requirements and how much of a role that will play in their decision. I could see it going either way here honestly.
It's all about the $$$ in the end, but I'm sure they're watching the legal battles on this front very closely to determine their next moves.