There are religious terrorists out there. There are also secular terrorists out there. For that matter, I suspect some terrorists are as sincere about their religious beliefs as politicians are about their campaign promises.
There are also right wing terrorists, left wing terrorists, anarchist terrorists, and people with no coherent ideology who just want to blow up things and hurt people. Terrorists can be of any race or ethnicity.
Terrorists can look like anybody. Even elderly and disabled people have joined these movements. So anybody can be mistaken for a terrorist. Maybe a disgruntled neighbor might leave an anonymous type about you taking flight lessons or a chemistry class.
There are a couple of reasons why this will make us less safe:
1. When a suspect is captured, our justice system takes further steps to ensure that the right guy is in custody and the actual perpetrator is still at large. One of these steps is called a trial. Some people might insist that it is better to punish the innocent than let the guilty go free, but allowing people to establish their innocence helps ensure that guilty people do not go free.
2. Here's a hypothetical scenario. Let's say a bomb goes off in Chicago, and some group calling itself the Detroit Lions Liberation Army claims responsibility. The government arrests 10 Lions fans and doesn't give them a trial. Would this make Lions fans more or less loyal to America? Now replace "Lions fans" with "Southerners", "abolitionists", "African-Americans", "Mormons", "Japanese-Americans", "German immigrants" or any other group that has ever been placed under suspicion.