What protection measures to consider when switching many loads at the same time with shift registrers?
Disclaimer: I have no idea about the output current you're aiming. I can see nothing on the picture.

Since your gate resistor is pretty large, considering your application, you have to take few things into consideration.

If the MOSFETs are not over-sized, you're risking frying them, because the MOSFETs will operate temporarily, and many times per second, in their saturation region. On the other hand, if you application does not involve multiple switches per second, then that won't probably be a problem.

Don't forget to check if your driving voltages are greater than the MOSFET's Vgs which will make it operate in its linear region \$(Vds = Rds*Id)\$.

I should point out that you could simulate your circuit using LTSPICE for example, add you MOSFET's model, to see the temperature evolution with the expected switching patterns.