LaunchKernels[3]

<<xAct`xTensor`
ParallelNeeds["xAct`xTensor`"];

Off[General::spell]
Off[General::spell1]

DefManifold[M,4,{α,β,γ,δ,η,λ,μ,ν,ρ,τ,χ,ω,ξ,ζ}]

DefTensor[B[μ],M]

DefMetric[1,metricg[-μ,-ν],CD,PrintAs->"g"]

DistributeDefinitions[CommuteCovDs]
DistributeDefinitions[SortCovDs]

list1={CD[α]@CD[β]@B[γ],CD[β]@CD[α]@B[γ]}

Map[SortCovDs[#]&,list1]

ParallelMap[SortCovDs[#]&,list1]

Map[CommuteCovDs[#,CD,{α,β}]&,list1]

ParallelMap[CommuteCovDs[#,CD,{α,β}]&,list1]