Can you be spiritual without being religious? Can you be spiritual and also scientific? Of course. It depends on what is meant by spirit.
A Google search produced this definition:
1. The nonphysical part of a person that is the seat of emotions and character; the soul.
2. Those qualities regarded as forming the definitive or typical elements in the character of a person, nation, or group or in the thought and attitudes of a particular period.
Obviously the first definition -- the non-physical part of a person, soul -- implies a religious sensibility. Or at least, a supernatural one.
But the second definition -- the definitive elements of something -- allows for a broad range of interpretations about what spirit signifies.
When I read Albert Einstein's letter to a girl who asked him if scientists pray, and if so, what they pray for, I sense that Einstein was thinking of spirit along the lines of "definitive elements." Read the letters, and see what you think.
(Source: Dear Professor Einstein; Image: Albert Einstein in 1947, via Life.)
The Riverside Church
January 19, 1936
My dear Dr. Einstein,
We have brought up the question: Do scientists pray? in our Sunday school class. It began by asking whether we could believe in both science and religion. We are writing to scientists and other important men, to try and have our own question answered.
We will feel greatly honored if you will answer our question: Do scientists pray, and what do they pray for?
We are in the sixth grade, Miss Ellis's class.
January 24, 1936
I will attempt to reply to your question as simply as I can. Here is my answer:
Scientists believe that every occurrence, including the affairs of human beings, is due to the laws of nature. Therefore a scientist cannot be inclined to believe that the course of events can be influenced by prayer, that is, by a supernaturally manifested wish.
However, we must concede that our actual knowledge of these forces is imperfect, so that in the end the belief in the existence of a final, ultimate spirit rests on a kind of faith. Such belief remains widespread even with the current achievements in science.
But also, everyone who is seriously involved in the pursuit of science becomes convinced that some spirit is manifest in the laws of the universe, one that is vastly superior to that of man. In this way the pursuit of science leads to a religious feeling of a special sort, which is surely quite different from the religiosity of someone more naive.
With cordial greetings,
your A. Einstein