No. This new law will almost certainly be overturned. Frankly I personally have no problem with an individual having a religious exemption as long as there is full time other individuals in the same office or business who will do the job. In general the only person who I think can, in good conscience, use the religious exemption to refuse service is a clergy member. If you are a govt employee charged with certain duties you should be willing to do those duties...if you are a private business licensed to serve all the public you should be required to serve ALL of the public. Nobody is forcing you to stay in a job you have moral objections to.
Do you think a Muslim born in Saudi Arabia who lands a job with the DMV should be exempt from issuing licenses to women on religious grounds?