Two out of the three sections of H.R. 6784 (the "Manage our Wolves Act") have clauses stating that they aren't subject to judicial review (I suppose Congress is fine with having the judiciary muck about with the short title of the bill). This can't possibly be the first time Congress has tried to exempt a law from judicial review, so how common is such a thing?
The statute in question isn't doing what you think it is doing.
There are two ways that one can judicially review a regulation.
One exists solely by virtue of the Administrative Procedure Act, which allows members of the general public to bring a lawsuit alleging that the issuance of the regulation violates the requirements of the Administrative Procedure Act (e.g. arguing that a hearing wasn't held as required, or that an environmental impact statement was not prepared). What Congress is doing in the linked statute is effectively waiving the Congressionally created procedural requirements for issuing new regulations under the APA by prohibiting the judicial review of the issuance of those regulations that would otherwise be available under the APA.
The other way for someone to challenge the validity of a regulation, for example, by asserting that it violates the constitution, or that it is contrary to a statute enacted by Congress, is for someone who is actually harmed by the allegedly invalid regulation to bring an challenge to the validity of the underlying regulation, rather than merely to its issuance, in a situation involving an actual case or controversy.
The statute does not waive that kind of judicial challenge to the regulations and could not do so even if purported to, although Congress could limit that judicial review to one court (e.g. the Court of Appeals or the Court of Claims) rather than another (e.g. the U.S. District Courts). This is the kind of challenge that Marbury v. Madison involved, and the right to bring that kind of challenge is inherent in the structure of the constitution, rather than arising by virtue of a statute.
Actual attempted waivers of Marbury v. Madison type judicial review do happen, but are very rare. Waivers of the statutorily created APA judicial review of newly issued regulations are uncommon, but not nearly so unusual.