If you are reliant on prescribed medication it can be an issue but the underlying cause for the dry eye may be an issue in itself. If it's a blocked tear duct, then maybe it's worth investigating whether it can be sorted.
Ultimately you shouldn't let it put you off applying, but it may require further investigation before you can be passed fit to enter.
The medical standards cannot cover all individual issues, but the things you need to think about are the unique service environments a sailor is expected to serve within.
In a Chemical, Biological or Nuclear environment, exercise or real, you could be required to wear a respirator facemask for several hours. Similarly, during firefighting operations you could be wearing breathing apparatus for prolonged periods.