It's possible to do Whole30 without eggs. If you're having trouble finding recipe ideas, Google Whole30 AIP recipes -- AIP (autoimmune protocol) is a more restrictive way of eating than Whole30, sonthere will be other things those recipes leave out that you can still have, like potatoes, but they should also leave out eggs.
For the meat, I would focus on the ones you do like. For the ethical concerns, it can be more expensive, but you might feel better about your options if you try to source animals that are raised well -- pastured or grass fed or free range. See if you can find local farmers that sell meat they've raised. Sites like http://Www.Eatwild.com may help you find some. For texture issues, it might help to hide the meat in casseroles or make fish patties/cakes (this is one place the AIP recipes may be really helpful since these usually use egg as a binder).