On the first day when I was being introduced one of the gentlemen ignored/refused to shake my hand and I believe we both felt embarrassed and slightly offended. I have learned that this man is devout. I wish to know what issues might cause concern. I wonder about the fact that there is only one washroom for both men and women. Also, I wonder about my wardrobe choices particularly in the summer months (sandals without nylons) and when we need to go outside to look at a site (sleeveless top). One warm day I took my business jacket off (as did all the men) and was wearing a sleeveless blouse and noted that he did not contribute to the discussion. He is a star performer and I wish to enable both of us to obtain our best performance and productivity in a comfortable working environment. Any input or suggestions are appreciated.
There are so many different believes and sects within those that you will not come to any results on your own.
You will need to ask them.
Schedule a meting with them, tell them in advance what you told us, so they can prepare and listen to what they have to say. As they may not follow the same religious guidelines, you should schedule a single meeting with each. It goes without saying that for this meetings, you should err on the side of caution and dress very conservative.
Make sure you tell them that you will try to make it work. In the end, you will need to decide what exactly is worth it to accomodate them and what is not. You are running a business (or have been employed to do so). If religion gets in the way of said business, you will have to make some tough decisions.
If you are not a Muslim, then you don't need to live under Islamic rules regarding clothing, or anything else. The workplace is not for religion any more than it is appropriate for politics or other irrelevant personal things. For example if you had an employee who was anti-semitic, would it be your responsibility to make sure they never had to work with any Jews? Of course not, it's the employees responsibility to act professionally and leave their ideological issues at home.
You already know how to handle this situation. If they were homophobes, racists, or misogynists I doubt you would be asking this question, because it's a no-brainer. Treat everyone equally, and handle unprofessional behavior stemming from religious ideology the same way you would handle it coming from anywhere else.
It's quite likely that the two gentlemen in question have more experience in contact with members of a different religion than you have, and quite possible that they take their religion more serious than you do.
We assume that you have no intentions to hurt anyone's feeling, but on the other hand it will happen due to lack of knowledge. I think you should make it clear to both that if you do anything that conflicts with their religion, they must not suffer silently or get annoyed with you, but MUST tell you what the problem is so that it can be fixed.