I never soaped with animal fats in the beginning, and only do a few now for family. However for the most part, I don't use them at all. I still haven't used tallow. I bought some to make soap for my brothers and to see what it's like to work with but just haven't got around to it yet.
I started out using the cocoa butter and shea as my hard oils mostly. CO of course as well. In 2016 I started learning about using Soy Wax in soap and now use it in most of my soaps, up to 30%. Another soaper here uses it at 40%. My mix usually still include Cocoa Butter and Shea as well. I had a little mango butter and it was also great in soap, but I haven't purchased any since, so it hasn't been a regular ingredient. I'd like to get some again and compare.
Many people have a real problem with palm and feel it is ethically wrong to use even when certified from sustainable growth. Some will use it and some won't. Some sources suggest palm oil it is suitable for vegans, because it in its pure form it is completely vegetable, but there are opposing views on the subject.
Each person must decide for themselves where they stand on the palm issue. Here are a couple of views from differing perspectives:
https://www.plantbasednews.org/learn/palm-oil-vegan
https://legacyofpythagoras.wordpress.com/2015/05/26/palm-oil-is-vegan/