People normally associate think of the workplace as a place of spiritual neutrality. In fact, there are obvious legal concerns in trying to imbue a workplace with a religious expectation. 

But there's a difference between religion and spirituality, and I would argue that spirituality extends beyond any formal religion. I believe a company culture that embraces spirituality is a company that values the full spiritual depth of those who comprise the organization.
Setting religion aside, there is a spirit of community and interaction that arises in any organization. It's merely a question of what it becomes. It emerges as a result of the ethics, passions, and empathy exhibited by employees within the organization. Another factor is the degree to which leadership welcomes the fullness of each human being who happens to be their employees at the time. And it has something to do with how much leadership encourages employees to know each other in this way, as well. 

Making spirituality part of your culture
The art of developing a spiritual workplace involves far more than perfunctory meet-and-greet introductions for a new hire, or team-building exercises where people mention a few bullet-point interests in their life outside work. These things alone won't make an employee feel they can actually be themselves with their team (let alone their manager). They want people they work with to know the full story of who they are, or what they want out of their employment or their life. 

Someone's full reality consists of knowing the answers to potentially intimidating questions, such as these: 

Are they passionate about their role and/or the company's mission? 
To what extent is their job merely a means to a financial end versus a genuine passion? 
If money was no issue at all, what would they be doing with their time on earth?
If an employee worries that answering these questions the wrong way will get them fired, or ruin their chances for advancement, they may only give you the answers they think you want to hear. 

Every employee is showing up to work for some reason. Getting to know why can be an exploration of supporting them holistically, and it often creates an outpouring of sincerity and connection that they've never offered (or felt) before. 
It also can create an opportunity to assess and improve their spiritual alignment within the organization. That may take the form of reconfiguring their role in a way that still adds value to your company. It may even be alerting them to a job opportunity outside your organization where your connections can steward a better opportunity for them. 
Sure, there's realistic limits in trying to help all employees in all circumstances of misalignment, but the rule of a spiritually misaligned worker should be solvability, and if they sense that is your aim and the aim of their peers, it goes a long way in setting the richness (or coarseness) of company culture. 

Benefits of spirituality in the workplace
Embracing the spiritual fullness of the people in your organization is not only about healthy ways to minimize misalignment or discontent; it's also about ways to maximize collective intelligence. When team members feel embraced by sharing their strengths, weaknesses, and motivations, the role for people on each work project becomes virtually self-evident to everyone. They also feel more responsible for each other, because the richness with which they know each other engenders a greater sense of doing well by one another. 
The healthiest organizations have people who feel seen and valued for who they are and what they desire their life to become. At Neurohacker Collective, we've strived since our founding to create a sincere sense of community between our employees. This extends, in turn, to our employees enthused to build a true sense of community with our customers. 
There's a lesson in that. The entire arc of culture that an organization brings into being, begins with respecting the holistic totality of the beings within it, including the spirit of who they are beyond employment.