A question about circuit design with a multivibrator
The circuit looks fine to me.

You should mention where the I read that the input better not exceed 4V comes from. Indeed it is not advised to make any input voltage higher than the supply voltage. So if you supply the IC from 5 V you are allowed to take the inputs (all inputs!) up to 5 V. I do not understand why 4 V should be the limit for that.

The reason you don't want to exceed the supply voltage at the inputs is due to the ESD protection diodes as these start conducting when Vin > Vcc + 0.5 V.

By itself that is not an issue (it will not damage anything) as long as the current (into an input and through the ESD diode) is limited. You took plenty care of that with R4. So as far as I am concerned you can remove R2 and D1 as R4 by itself protects the input more than enough already. But R2 and D1 also do no harm so it is your choice to remove them or not.