I must not know how exactly to describe what I'm looking for, since I can't find much currently on Google. I'm using ArcGIS Pro desktop. I would like to vary color by one attribute (vegetation class) and texture/image/hatching by another attribute (canopy density class). How do I go about it?
Look at attribute driven symbology and Symbol Property Connections
It will allow you to vary some attributes, such as symbol color, outline width and transparency if you have fields in your data to specify what they should be. Like life, you can't control everything.
I used a set of test polygons with three attributes to drive symbology {class, color, width}.
I set the symbology initially to a single symbol using a 10% hatch.
Then enabled allow symbol property connections:
Navigate to symbol properties, a database icon appears next to what you can control:
Here, color is driven using the color field, and outline width is using the width field:
The hatch (pattern) separation is controllable, as is the angle, so I set those using a custom formula (where angle = width *45 and separation = (width * 2) + 5) kinda silly, but you get the idea). Then set the hatch color to the same color as the outline:
I think I could have used a thematic map to set the symbol style to unique values so you may not be limited to one symbol type, but then you'd have to plug in the attributes to drive each.
Notice though, that the legend does not reflect any of this. You would have to devise a creative solution for communicating the meaning of colors, angles and thicknesses to the reader.