I just went through this recently because I wanted my own term life insurance policy to supplement what work provides. The only company I found that was willing to insure me as a climber was Prudential. I was honest about my climbing so I had to fill out a climbing addendum and I have to pay more each month. In addition, I'm only covered for climbing up to I think 600 feet, which is fine for the majority of the climbing I do. I was able to get a 20 year term under these conditions. The one thing you have to realize is that insurance companies do not know the difference between rock climbing and mountaineering. My impression after going through this process is that rock climbers are getting punished for deaths related to high altitude mountaineering. In any event, I would check out Prudential.
I have a standard term policy with American General. The questions specifically asked about mountaineering, which I do not engage "on a frequent basis" (or like, at all). Skydiving was also asked (just for reference in terms of objective danger). When I asked about these, it was explained that just because you checked "no" doesn't mean you could never do those things.
I am a Life Insurance Producer for the state of Colorado and I've been doing this for some time now. Most carriers don't like the apparent risk of climbing so it's either an auto-decline or a bunch of extra paperwork and a higher premium. I work exclusively with a Carrier that specifically insures people with high-risk occupations so rock climbing and mountaineering are no sweat.