Matching the impedance of a filter?
You WILL have to consider the output impedance of the driving chip AND the input impedance of the receiving chip when you design your filter or you will likely get disappointing filter performance. All your good work using high Q inductors could be ruined with an output impedance as high as 50 ohms - this resistor is in series with the output effectively and, if you are using series inductors in your design, the first stage will be massively affected if not taken into account.

On your last filter stage, the effective parallel resistance of the receiving chip being 50 ohms may also ruin that stage's abilty to be high Q.

Regards matching the nominal pass band impedance of the filter to the two IC's 50 ohm impedance I'd be less worried. 300MHz has a wavelength of 1m and you are not going to get standing wave problems on a few inches of circuit or bread board. Clearly don't make the filter's input impedance too low and don't make its output impedance too high or you'll have significant insertion losses (irrespective of whether the chips "ruin" the filter characteristics).