But the BBT is a theory that attempts to explain redshift! So any other theory of redshift is an anti-BB theory, and this thread is about non-anti-BB ATMs...or so I was led to believe by the OP.

As an example, take the electric-sun thread. The electric-sun theory is non-anti-BB. However, the mainstream theory that the sun is powered by nuclear energy is on "pretty solid ground," so the electric-sun thread is probably not going very far. By contrast, the theory that the expansion of the cosmos was powered by Inflation (thus explaining the redshift), is is on shakey ground. And that soft earth is fertile ground for alternate theories.

Alternate theories--outside the BB--are like weeds trying to grow in granite.