No. Because, like I've said over and over again, the act itself would not be banned. What should be prohibited is intentionally causing people distress - in which case, it doesn't matter what the act is, it only matters about the intent.
This is in fact a fairly high bar to meet. It would be very difficult in many cases to prove intent. Sometimes people make their intent clear, though, either directly with what they say or with the specifics of how they act.
Promoting non-belief would easily not be banned, because you're doing it for the purpose of sharing your beliefs - in exactly the same way a religious person preaches. Burning a cross in your back garden also would be fine, so long as you weren't directing it at a specific Christian with clear intent to upset them. Burning a cross in public would likely be wrong, though, as you can't reasonably argue that you weren't trying to target some Christians out on the street to upset.
Substitute religion and religious symbol as you see fit. I'd also draw a comparison to flags and war memories, those are already protected under law in the nation they represent. This makes sense, the people making the law say you can't descecrate their symbols, just like a religion makes its rules. The reason behind this is because it is disrespectful. Is it really that much bigger a leap to say that you shouldn't damage other peoples' symbols either - particularly when the only reason you're doing it is to be disrespectful?
Like, I don't think throwing a flag on a fire is inherently wrong, however burning a flag in front of a load of war veterans on Rememberance day is definitely wrong. One is just burning something, the other is done with clear malicious intent. But the law would say both are wrong here, yet none are wrong with other symbols. The law doesn't quite fit.