Can tenants legally opt out of pest control in an apartment building in Los Angeles?

Yes you have the right. She also has the right to say no. Who is right depends upon the rental agreement. Each paragraph in a written rental agreement is referred to as "a covenant" (a written promise). If one of the covenants deals with pests or access, then your approach is to serve a Three Day Notice to Cure Covenant or Quit demanding access to the unit for pest control purposes. If she fails to provide access after the notice expires, evict her. Now, your tag indicates Los Angeles, so the next issue here is whether or not the building is rent controlled. That is fairly easy to determine. If when your tenant dials 911 the Los Angeles Police Department appears at the door and, the building was constructed before 1979, it's rent controlled. Failure to permit access is a violation of the rent stabilization ordinance (LAMC 151.09A2 to be exact) and again, you provide her with a three day notice to cure covenant or quit. Remember, that in a rent controlled jurisdiction, that type of notice must provide the date of the occurrence, who witnessed it, what time of day it occurred, what the actual violation is, and what the tenant has to do to cure the violation. Again, if she fails to provide access after three days, evict her. If you are not in a rent controlled jurisdiction, and if she's been with you less than a year, give her a thirty day notice of termination of tenancy. If over a year, give her a sixty day notice. There is no need to permit her to dictate how you're going to manage your unit.