Now that we have that clarification, the answer is it depends on which Fidelity index funds you use in your current 401k.
Many people, including myself, are of the opinion that two index funds that track the same index are substantially identical (ie, can cause wash sales). AFAIK neither the IRS nor any tax court has ever ruled on what substantially identical actually means.
If you agree with this definition of substantially identical, then the fact that you have Fidelity index funds in your 401k is not what's important---it's the indices they track that is. If I recall correctly, Fidelity's total market index fund tracks the Dow Jones US Total market index, which I'm pretty sure no Vanguard fund tracks, so you'd be safe with that fund.