I was a Running Start alum as well (along with many of my friends). If you're in Pullman, you can take courses at Washington State University. It was incredible for me - for my friends who went to UW or WSU after graduation, they got 2 years of college credit and many graduated early. I went out of state and was able to skip introductory courses, and having already been to college in high school meant I was way more mature than many other students.
Honestly, for the cost of the program, it is extremely impactful. I didn't feel like I missed out on high school much either - I still took half my classes there.
I guess to counter the idea that it hurts on college applications: I can't say anything definite, of course, but I'm fairly certain taking physics at WSU looks much better on an application than taking your high school's physics. You look like a more ambitious and capable student.