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It would be great if more rescuers began rescues and registered for 501(c)3 status. Lawyers and accountants - which I am not - could best advise re the many benefits to legally becoming a nonprofit. We certainly need lots more rescuers and good placements. When they establish accepted management practices early on, that is commendable.
In general, I feel more comfortable networking for 501(c)3 organizations than circulating for non-501(c)3s. When a rescuer operates as a business, even at a loss, it is still not an actual nonprofit as I see it. Sometimes rescuers will say they wish they were 501(c)3 so that they can receive grants. There are however a long list of other virtues to becoming a 501(c)3 organization. It is beneficial for any donors who wish to receive a tax deduction, which might lead to more donors more regularly and contributions in larger amounts. It can lead to more accreditation with other organizations. There are more opportunities to officially rescue shelter pets. There are discounts offered by vets and other professional services and vendors. It is easier for people interested in possibly supporting the effort to vet the rescue organization. Many articles at such sites as Petfinder list several more advantages.
Of course, there are different networking scenarios where this doesn't apply. For example, when a person finds a stray and is looking for a rescue organization, I am not saying that networking the finder's post is not a good idea because they are a private individual. It certainly is, but, again, in an ideal world what makes sense to me is to try to find them a 501(c)3 to rescue the pet as opposed to an independent rescuer.
Finally, being 501(c)3 doesn't automatically result in a rescue organization being a high-quality placement for pets or even that the group will achieve financial solvency through this step. Being a business doesn't necessarily mean a rescuer is bad either. Obtaining credentials is simply a constructive early step in setting up a rescue. An alternative would be to be closely associated with an established 501(c)3 as a volunteer. In my opinion, being officially aligned with a 501(c)3 or going through the steps to obtain the status oneself enhances a rescuer's reputation and is fundamentally better all around for pets, rescuers, fosters, and adopters.