I am writing my physics PhD thesis and I did not study fluid mechanics (other than the few chapters in the standard general physics).
It will really be dependent on what is your physics field but you can definitely survive in physics without deep knowledge of fluid mechanics except when your study require it
A professor remarked that it was a bit sad that physics students nowadays have a better understanding of quantum field theory than fluid mechanics. He mentioned this while lecturing on QFT.
Agreed, I studied Materials Engineering - Fluid Dynamics was one of the hardest subjects in my opinion. I liked thermodynamics it made sense to me, solid mechanics was a bit of a slog to get through (endless amounts of beam deflection) but fluid dynamics arrghh.
I chose to take a particle physics course as an elective in my final year - I was planning to specialize in battery and capacitor technologies and wanted to learn more.
The lectures were very different to Engineering much, much more theory focused(almost nothing on applications) it was my introduction to things like Hamiltonians, Wave Functions and Fermi-Dirac statistics. I'm glad I took the course I learnt a heap especially about semi-conductors it gave me a better appreciation and understanding of things we covered in my engineering degree like magnetism and phonons/heat transfer as well. But I will say it did feel like another world compared to Engineering - there was much less in common than I would have thought.
There is a more practical reason for that. QFT has become essential to learn for many Condensed matter physicists. And they always are with particle physicists which will span most of the physics community, at least comparing with whose work involve in-depth knowledge of fluid mechanics. Not to mention that QFT seems easy in comparison.
It will really be dependent on what is your physics field but you can definitely survive in physics without deep knowledge of fluid mechanics except when your study require it
PS: I am a particle physicist.