Democrats say contracts of adhesion (the form contracts you agree to every day with various providers of goods and services), because the consumer has no power to negotiate them, should not be able to require arbitration, which cuts off class-action rights of potential plaintiffs and shuts down potentially successful litigation on a technicality. Because such harms are often very small to individual plaintiffs (but large as a whole because of the large number of consumers in the economy), cutting off class-action lawsuits essentially leaves consumers without legal recourse.
Republicans say that class-action lawsuits mainly benefit the lawyers who bring them rather than plaintiffs or society at large and are often spurious and designed to extort settlements from companies that prefer to pay a settlement than risk a very large judgement, and the costs of such settlements and defending against class actions more generally lowers share prices and also increases the prices of goods and services, especially goods and services that are particularly likely to attract class-action litigation, and ought to be discouraged or prevented by any means possible.
The rest is just acting to reflect these policy preferences.
The debate is not really about great consumer harms, the sort for which a consumer might actually bring an individual lawsuit, although these are also restricted to a lesser degree by arbitration since arbitrators are, generally speaking, more predisposed to favor corporations than judges, and arbitration usually forbids punitive damages and otherwise restricts certain types of damages that a court might award. But the main action is about consumer harms that are small individually but large in the aggregate and whether those can be brought as class actions.