Hey Jim,
The Ten Commandments say to Honor your father and mother.
You would not have a funeral mass for them, but you would take part in respect for your family. Funerals are to show respect and love for the present and past.
The common bond is that of love. Love of God and love of each other. To do less for your parents would leave your heart in pain and frustration for the rest of your family.
It may be more difficult if they are JW or such, but even there it is more just a gathering and some reading.
But, to be there is to evangelize and share your faith, just by your being present.
God bless you!
By the way, my dad is Southern Baptist and is 82, I know I will be facing his time to go home also before too many years have passed.