Organized groups striving for power
I believe that the threshold of a civil war is crossed when there are multiple competing governments (or government-like organized groups) at the same time who all aim to take power in the same country in a violent conflict.
Obviously, if there's no violent conflict, it is not a civil war.
If the scale of the conflict is low, it is not a civil war. For example if a community of 100 people rebels, fight against the army, and all of them get killed deaths, that's horrible but that's not war. The boundary is generally set at 1000 deaths in a year, or, conservatively, at least 100 deaths on each side, so if there's 500 insurgent deaths and 23 dead government soldiers, that's below the line.
If one of the two parties is not local, then it's not a civil war, that's normal war.
If a government is replaced by another government, but there's no stage where both old and new governments have de facto control of at least part of the country at the same time no matter how, that's not civil war, that's something else - a coup or a revolution or voluntary handover, depending on circumstances.
If one of the parties does not make a claim to leadership of the whole country but explicitly claims only part of it, then that would more accurately be named as a war of secession or independence, but that's usually treated as a type of civil war (e.g. American Civil War).
If a group is not well organized, if it does not have leadership, self-governance and some intent to actually govern whatever territories and people they (perhaps temporarily) control or will take control of, then that's not a civil war, but a riot or disturbance.
If the opposition is not well organized, that's also not a civil war - for example, if well organized paramilitaries are performing a mass slaughtering some minority, that's ethnic cleansing or genocide, but not civil war unless that minority is fighting back in an organized manner instead of as scattered individuals. If only one party is applying organized, systematic violence, it's not a civil war, that's generic application (assertion?) of sovereignty and monopoly on violence. War needs two or more opponents like that.
So if we look at the current USA situation, then that seems definitely not a civil war according to these criteria. If we consider "protesters" and "counter-protesters" (as described in the original question) as the hypothetical parties to such a war, then both of them (a) don't meet the criteria for organization and leadership; (b) aren't currently taking over governance of any area or population, but still acknowledge the power of the current country/state/city leadership even if they current leaders are their opponents.
The boundary would be crossed when you either have an alternative government or are trying to build an alternative government that does not acknowledge the competing government as legitimate, and that governance is violently contested. I would say that USA is in a civil war if either "protesters" or "counter-protesters" would assert control and governance over some territory and the other group (as an organized group!) or the current government would violently contest it with significant casualties.
The closest thing yet IMHO was the Capitol Hill Autonomous Zone - if there was a sufficiently large organized group that would try to violently retain control of it, then that would be a direction to civil war. But as long as it's just angry mobs without self-governance, occassional unorganized, unsystematic violence, limited numbers of dead and no attempt to violently enforce your policies and governance on others, it's far from a civil war. And let's hope it stays that way, as real civil wars are very, very horrible both for participants and bystanders.