If cell in column contains value, clear contents of another column in the same row

You can use AUTOFILTER for things like this. This should get you there, or close enough for you to finish:

Option Explicit

Sub FilterOutFALSE()
Dim LR As Long

With ActiveSheet
    .AutoFilterMode = False
    .Rows(1).AutoFilter 3, "False"
    LR = .Range("A" & .Rows.Count).End(xlUp).Row
    If LR > 1 Then .Range("A2:A" & LR).Value = ""
    .AutoFilterMode = False
End With
    
End Sub