Should a Muslim follow one madhab strictly?

This is not necessary at all. Whenever you see a difference of opinion between two madhabs, study the reasoning of both and adopt the one you find as more convincing to your intellect. A person should entirely base this acceptance on reasoning and not on desires. The greatest judge of this is one’s own conscience. If you accept a point of view because it would be easy to follow, in spite, of being intellectually convinced against it, then this, certainly, is not the right attitude.

Also, if a person is not a religious scholar, he should refrain from forming his independent opinion. He  should only select between the existing ones.