Sure. The First Amendment was only meant to be a suggestion, not a right. It's ok if the Government contacts a publisher, or a forum, and tells the moderators to censor ideas and posters it finds disagreeable. It that your sense of what this fight is about?
The first amendment was against government censorship, not private places. You going to the town square or publishing something against them. If you’re concerned about censorship, talk to the thousands who have been zotted from here over the years. Some deservedly. But zotted none the less.
That's not what happened to Woods and not what he's complaining about.
A private organization, the DNC, contacted another private organization, Twitter, and asked for content to be reviewed.
There was no government involvement and no 1st Amendment issue.
Here’s what progs are saying about govt Twitter cooperation.in 2020 Trump was POTUS not Biden. Is working in cahoots with DNC working with govt? It can be argued that it is not. The DNC is not a govt organization. It is defensible to see these joint operations and say they were not speech limitation by govt and therefore not a 1st Amendment violation. Of course the FBI participation raises other issues.