The government can't compel a business to act, but they can punish them for not acting. Punishments may range from fines, to having to pay damages, up to being arrested or forced to shut down, but it's always the option of the owner to accept those punishments instead of changing their behavior.

As to the question of whether the government can punish a business which refuses service to a protected class based on a religious position, that's still an open question, and will vary state-by-state. For example, in California there's a state Civil Rights called the Unruh Civil Rights Act which prohibits arbitrary discrimination.

Until it gets to the Supreme Court, there's no way to provide a more definitive answer.

The government can't force a business to act, but they can punish them for not acting. The threat of punishments (which may range from fines, to having to pay damages, up to being arrested or forced to shut down) may compel the business to act (in the sense of "apply pressure to act"), but it's always the option of the owner to accept those punishments instead of changing their behavior.

As to the question of whether the government can punish a business which refuses service to a protected class based on a religious position, that's still an open question, and will vary state-by-state. For example, in California there's a state Civil Rights called the Unruh Civil Rights Act which prohibits arbitrary discrimination.

Until it gets to the Supreme Court, there's no way to provide a more definitive answer.