The fee to ride the bus/train is not called a tax, why would this be any different?
Roads need to stop being subsidized, it's the only thing that's going to give mass transit a chance to actually compete.
It's not regressive because charging someone to use something (like police services) is not a tax, after all.
The very point is that right now roads are paid by taxes, which are progressive, and people are suggesting replacing them with fees, which are regressive (without some additional scheme to account for this). A better solution would be subsidizing all public transit so it is free, which is progressive, not regressive. But will never solve the problem because it only incentivizes the poor to use transit.
If we stop subsidizing roads or make public transit free/cheaper then roads will be for the rich only, and public transit I'm sure will have millions poured into it and flourish. The government is, after all, historically very responsive to needs and pain points that are only felt by the poor and minorities.
We need to provide funding for transit first. We need to get middle-upper class people riding it, people who vote, are white, donate to political campaigns, know powerful people, etc which specifically means making it fast, efficient, reliable. Look at places like DC and NYC and SF/bayarea where middle-class businessmen take transit because it's the easiest, most efficient method and is fairly reliable.
On the other hand, if you're replacing income tax with tolls or just raising tolls without lowering other taxes, then it would be regressive.
We're talking about two things at the same time: 1) A method to reduce traffic, 2) A method to move money from people into toll-road owners.
Systematically transferring money from the overall population to a subgroup is generally thought of as a tax.