You have elevated the risk of death and injury unacceptably
Criminal laws exist to keep people from committing actions that society has deemed to be unacceptable. There are plenty of other laws but criminal laws in particular is all about stopping people from doing things we do not want anyone to do. Most of these criminal laws concern damage/injury, to a persons body, mental state, honour, economy, property, rights... and they concern the injury after it has happened.
Some criminal laws however are about recklessness, where injury has not actually occurred, but where you nevertheless have needlessly — and unacceptably — elevated the risk of injury. Reckless endangerment for instance is one such example.
Speeding falls into this category. Speeding is a form of reckless endangerment. We know it is endangerment simply from science and statistics: increased speed lowers available reaction times; makes it harder to exercise control over the vehicle in an emergency (like having to stop before a sudden obstacle); and increases the amount to destructive energy and force in case of a collision/rollover.
That is the ethics behind this law: we punish and try to prevent recklessness before it does injury.
Is this arbitrary? Somewhat, but not entirely. And in any case, for every piece of road there has been a decision made: this is the maximum allowable speed here; if people travel at or below that speed, we are prepared to take the consequences of that and possibly find other methods by which to mitigate the damage done.
Most importantly, people have made the judgement call and said: "this speed limit is where we think that the danger will start to outweigh the use of travelling faster".
Now about your counter-examples:
Converting to Islam No, there is no-one — anywhere — that can point to that the risk of becoming a terrorist when converting to Islam is so great that this outweighs the human rights to freedom of thought and freedom of faith.
Transitioning to becoming male Again: no-one can point to any fact that says that existing as a male makes you unacceptably prone to crime.
Watching sports And again... you cannot find the facts for that, not in the same tangible and clear way that you can with speeding.
By comparison.... there are some other things — besides speeding — that we have deemed too risky and likely to cause big problems and/or injury, like playing around with explosives, toxins, and some weapons, or driving/piloting/doing surgery/conducting a train/practising law/operating a nuclear reactor without a license.
So the ethics is simply this: we — as a community — have made a judgement call, about where the limit is, the limit when need and utility no longer justify risk and injury.