The problem is that cyclists are public figures, and their work entails wearing uniforms that make them public representatives of the products and services that their teams exist to promote. And sometimes those products or services may be controversial and you're taking a calculated risk signing on the dotted line for said team. At the end of the day, it's not like Saxo Bank with CSC, or TotalEnergies with Ineos, where you sign with one sponsor and another joins the team mid-season so you're suddenly representing something completely different from what you signed up for. Adams has been very open about what his team is about from day one.
True, and I think it's worth noticing that pro cyclists are at the extreme of commercial sports.
At the other end we find athletes representing their country at, let's say, a world championship. There are a few sponsors, but nobody would doubt the fact that the relationship of these athletes to their team is defined by nationality much more than commercial interests (for example the national teams can't buy new riders/players).
In the middle, we have athletes representing a club - it could be a major European football club owned by a foreign investor, a big company. The foreign owner has big interests in the club and the players, but the players still primarily represent the club which has a quite well-defined geographical base.
The pro cyclist, on the other hand, is in a team that carries the name of a (multinational) company or organization. The rider is a living billboard - he is travelling around, saying to his surroundings "this product is really good - look at me, I'm a part of it". Now, if that product is controversial, this way of organizing athletes can backfire - especially if the teams start to have a political edge, such as promoting state-owned companies, or just carry the name of a country in the team's name.
Tbh, while I'm of course against unlawful actions, I do think cycling teams are a fair target for protests in certain political contexts. If the teams were called "Équipe Cycliste de Paris" or "London Bike Stars" or whatever, I would see it differently. I'd wish it was like this. Maybe some cycling historian will be able to tell me when and where it went "wrong".