Applying as a pre-nursing major or any other major for that matter, won't affect your chances of getting into CSULB. Your choice of major won't affect your chances of admission. Being a pre-nursing major is essential being an undeclared major. You need to finish certain classes before applying to their nursing program. There are 1,300 pre-nursing majors currently. Nursing is arguable the hardest program to get into at CSULB, but it's doable. I'll be starting nursing in the fall after taking 2 years to complete my prerequisites.
UCI has a direct entry program, unlike CSULB, which means you can apply as a freshmen as an actual nursing major so you can start their program as a freshmen and don't have to compete with other students. The same goes with UCLA. UCI and UCLA are already hard to get into, but getting into their nursing programs, which have limited seats, will be even harder. If you don't get in as a nursing major, you can also get into UCI or UCLA under a different major, and then later apply to their nursing programs after taking certain classes just like a CSULB.
The point is nursing is IMPACTED and difficult to get into EVERYWHERE in CA-- even those of CCs. If you can get into UCI or UCLA's nursing program, I say go for it. If not, choose a CSU. This may sound bias since I'm a CSULB student, but CSULB supposedly has one of the best nursing programs in CA. Their NCLEX (nursing licensing exam) pass rates usually range from 97-100% annually with close to 200 students taking them every year.
I hope this helps!