Telling people their beliefs are wrong and including a threat of trouble if they don't change or abandon them is evangelism.

Agnostics and atheists are notorious for not doing this. You, however, advocate precisely this in your description of how to treat converts. Therefore, you advocate evangelical agnosticism or atheism. That is, indeed, ironic.

Re: screening by questionnaire: Here's a little story:

My late mother-in-law was certified crazy by mental health professionals in three states. Every so often, she would be committed to the psychiatric ward because of things she had done. Every single time, the ombudsman would come to see her after a couple of weeks to ask her questions to determine whether she was competent to be released in her own custody. Every time she knew precisely what to say to convince the ombudsman to let her go. She was just as crazy, but crazy isn't the same as stupid.

Your screening will eliminate the overly scrupulous and the unsophisticated. It will not catch zealots, because zealots will already know how to answer your ombudsman. Crazy doesn't mean stupid.

Restricting people based on religion will only encourage people to lie about their beliefs and then experience a "conversion" later. It will not catch people with criminal intent because they will already have created a concealing identity for themselves. It's just like Prohibition: when you place unfair, overbroad restrictions on people, otherwise honest individuals will suddenly have an incentive to lie. It creates an atmosphere of mistrust and accomplishes nothing else.