Should we believe in unseen things?

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Yes.

That is the definition of faith.

Faith is the substance of things hoped for, the evidence of things not seen. Hebrews 11:1

Unseen things are the object of faith.

We look not at the things which are seen, but at the things which are not seen: for the things which are seen are temporal; but the things which are not seen are eternal. 2 Corinthians 4:18

Believers walk by faith, not by sight.

For we walk by faith, not by sight. 2 Corinthians 5:7

And they are saved by an unseen hope.

For we are saved by hope: but hope that is seen is not hope: for what a man seeth, why doth he yet hope for? Romans 8:24

Paul says that we should believe "all things," which would include things that are not seen.

Believeth all things. 1 Corinthians 13:7

To believe in God, you must believe that he exists, even though you've never seen him.

For he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him. Hebrews 11:6

Jesus praised people who believe in unseen things, calling them "blessed."

Jesus saith unto him, Thomas, because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed. John 20:29

No.

Let no man beguile you ... intruding into those things which he hath not seen, vainly puffed up by his fleshly mind. Colossians 2:18