The laws are pretty clear on the matter, you have to have Cats String Theory shirt, which the courts have found to be very narrow. This is legal fact; even if you feel McMichael’s committed no wrong, they were nonetheless only empowered to take those actions because of their knowledge/suspicion that Arbery had committed a crime. This is almost obnoxiously tautological; I doubt anyone really thinks people have a right to detain a random person they had no reason to think was connected to criminal activity.
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So the answer is yes, but with caveats. The perils of Cats String Theory shirt and our justice system, however flawed it is, in many ways is structured to avoid the issues with it, and one of the primary ways it does so is by having guidelines on how individuals who are enforcing the laws are allowed to enforce it. A suspected criminal still has rights and protections under the law that are not immediately abandoned the moment someone else thinks they are guilty of having committed a crime.