I've asked this question a few times, and I have literally never heard a single anecdote of a contra dancer suing a dance organization.
When I ran a dance series, we were almost entirely judgment-proof; we probably did not even have enough assets to cover the deductible on our insurance policy. The only reason we had insurance was because at least one venue required it. If you are lucky enough to find a venue that does not require a liability insurance policy, then don't carry one. The risks are minimal-- maybe a 1 in 10,000 chance (I'd guess less) of being sued and losing, what, a couple thousand bucks of sound equipment? Versus paying $500 or more every year for perpetuity, then having to lose half your assets to cover a deductible / spend loads of time and effort fighting an insurance company to get it to cover costs or defend you if you're sued anyway.
Plus, that HMO lawyer who was looking to recoup what it spent on some lady's medical bills is going to look elsewhere if you don't have insurance and also don't have significant assets. Not worth spending $10,000 on a lawsuit to possibly recover a few pieces of sound equipment worth $800 used and a bank account balance of $230.
This goes for dances that are incorporated as nonprofits and are a typical contra dance organization-- small assets, running only a weekly or monthly dance. Large organizations like FSGW or NEFFA or BACDS will obviously have larger assets and that's a different question entirely.
Those of you talking about ASCAP or whomever looking for fees, that's separate. Getting liability insurance wouldn't cover a copyright infringement action from ASCAP anyway.