I just got my engine back from my engine builder and I'm getting closer to installing it. I've also been talking to the previous owner about how he raced the car and he said that he never ran an alternator and never had any issues. The car has raced SCCA F & E Production since new. I plan to run SCCA and maybe Vintage or PCA. Is this still common or should I install an alternator?

I've never run an alternator in my FP car. Battery needs to be charged between each session. I use a big lead acid battery for ballast in the passenger compartment and replace it every couple years after all the deep cycling.
From a weight perspective, using an alternator and an Oddysey battery would be about the same as no alternator and a full size battery.
So the only benefit to no alternator is freeing up a small amount of engine power.

Thanks Chris. I'll probably continue to run without an alternator since I'm probably need all the power I can get running a 1.8 in F-Prod.

And being able to place the ballast where you want, as you pointed out Chris.