Every part of the First Amendment has been subject to "reasonable regulation" I would suspect upon investigation to find the right of assembly has too.
Now, you can argue that the rule, (because the Code of Federal Regulations or CFR) deals with rulemaking power of the federal agencies), is either "arbitrary and capricious" or that it exceeds the authority of the agency. These are legitimate challenges to rulemaking authority and can be appealed to the federal court system.
The First Amendment is pretty clear, "Congress shall make no law..." Yes, there are legitimate challenges, civil disobedience being one of them.
"If a law is unjust, a man is not only right to disobey it, he is obligated to do so." - Thomas Jefferson
Something tells me Jefferson would support the freedom of expression over "reasonable regulation."
Read Missourian's post concerning what the reasonable regulations might be.
"Congress shall make no law respecting the Establishment of Religion or the free exercise thereof....."
and you can't say a prayer in a public meeting any more. Tell me how that's "no law."
Their are several important aspects to Missourian's quote. One is that content can't be limited only "times, places and manners." The other is the standard of review for the regulation, it must serve an important state interest. That is a mid-range heightened review standard. Now, you might want to attack the standard of review and say that the feds should have to show a "compelling state interest" to curtail a Constitutional right, but the fact is there is regulation of Constitutional rights.
You can not like it and you can fight to change it, but that is the fact currently.