I wanted to donate to research which does not use non-human animals, so emailed ME Research UK to ask whether they did. They replied with a link to this page (indirectly) https://www.meresearch.org.uk/wp-content/uploads/2021/07/Standard-Grant-Conditions-2021.pdf which says "ME Research UK will not normally fund research which involves the use of animals." I campaigned for many years against animal research, including studying medical science to Masters level and challenging the head of science at my university, as it does not provide evidence for humans, and is grossly cruel (much more than is normally revealed). I was happy (for now) with ME Research's reply, so have donated to them.
I believe Invest in ME Research has never funded animal research either. Nor the Open Medicine Foundation, though they have used animal products in their research and might not have a policy against it. OMF have created a cell based model to mimic post-exertional malaise using human blood from patients vs controls (nanoneedle study). I believe that the thinking is to use cell based technology for testing, which will be much faster, as well as more accurate and far less cruel. There is also no "animal model" of ME.
There are models that are claimed to be animal models of "chronic fatigue", but they aren't very plausible/similar to real human cases.