3 Basic Steps to Reduce Personal Liability as an Org Leader

To expound on point 1, maintaining corporate protections is not a one-time deal. You also need to follow the required corporate formalities on an ongoing basis. 

For point 3, it could be rational to go without general liability insurance in some cases -- e.g., where the risk is low, the organization has little in the way of assets, and any person with potential personal liability has few assets without a substantial income. Being "judgment-proof" is a viable defense strategy, or at least "judgment-proof" enough that litigation would cost the plaintiff more than they could reasonably hope to collect. Whether having adequate insurance to cover risks borne by third parties is a moral obligation is an exercise left to the reader.

Other insurance considerations: if you regularly use your personally-owned automobile for business purposes, you should probably discuss that with an insurance agent in addition to discussing a general liability insurance policy. Also -- I think most EAs are in pretty low-risk lines of work for worker's compensation, but it is available (and sometimes required) for organizations with a single employee. 

Very late to this, but just adding that incorporating in Australia is relatively easy and inexpensive too (~$500 AUD, 15-20 hours). Ongoing compliance burden is low, and incorporating as a 'not-for-profit limited liability company' provides good legal protections.

The biggest downside is the limitations on the activities able to be undertaken by any charity, and if your charity is tax-deductible - the range of activities you can undertake is very much constrained.

Same general principles apply in the UK - a simple guide is here: https://forum.effectivealtruism.org/posts/ZwTrykpvztrF5FQQL/how-to-set-up-a-uk-organisation-limited-company-version

D&O insurance should be a consideration as well.

Out of curiosity, have any of the major EA orgs been involved in any lawsuits to date? I've never heard of any, but even if there have been none, we can't assume there never will be.

I know most are hesitant to start an actual non-profit since that is more expensive and time-consuming, but at the least, you can form an LLC.

It may be better to seek fiscal sponsorship from a relevant existing non-profit org.

Note: Liability insurance works differently in different countries. For example in the US if I work as a doctor for three years and pay premiums for liability insurance during those three years, then any liability for any actions during that time are covered forever. If someone sues me for something that happened during that time period after I've retired I'm covered because I paid premiums during the time of the incident.
In other countries you are only covered if you have paid for insurance during the time period that you are sued. (They have additional policies to cover you after you leave a job or profession.)