If you can't find a mutually acceptable method of communication, there will be less (or no) communication. The price of that is, at minimum, that you get less information; it may mean missing events because you don't hear about them, or people being annoyed that you didn't either come to something or let them know you wouldn't.
I tend to cut more slack for people who *can't* use a particular method of communication. If someone has carpal tunnel or bad arthritis, I'm not going to insist that they use a text-based communications method. Conversely, my mother and I communicate mostly by email and online chat, because she has a hearing impairment and the hearing aid and telephone don't work well together.
But if you're willing and able to talk on the phone, but dislike voicemail, your best bet is to leave an outgoing voicemail message that says something like "Hello, this is LadyL. I don't listen to my voicemail very often, but if I recognize your number I will call you back." And then maybe check for messages if there's a missed call from a number you don't recognize.
This assumes that most people would be okay with "Hi, this is LadyL. I saw you called. What's up?" even if they'd left a message that had the basic news/question in it. It's not perfect, but it might work for meeting each other halfway.