With changes to Blender 2.8’s material and real-time systems, a materials ‘diffuse‘ colour, the Base Color of a node-based material, only appears when the 3D View is set to LookDev or Rendered modes, for Solid mode meshes appear white, making a mode switch to LookDev or Rendered necessary for an ‘at-a-glance’ assessment of material assignments – what material is assigned to which mesh or mesh parts. Despite this it is possible to change mesh colours without effecting material assignments in Viewport Display.
Design note: see here for more on the basics of node-based materials.
To change the colour of a mesh without affecting any material assignments, select a mesh then in Material Properties access the Viewport Display options (collapsed by default). Here, click the Color sample field, white by default, and select/set a colour from the wheel that appears – as the colour is changed the mesh will update in the scene.
Design note: using standard materials, i.e. Use Nodes is disabled, the materials Base Color will override the colour set in Viewport Display.
When using node-based materials if the mesh colour and material colour need to match, click the Base Color sample and note the R, G, B (or HST etc.) values associated with the property. Once done, in Viewport Display, click the colour sample and type the sames values as the R, G, B inputs for Color, duplicating Base Color.
Design note: unless Use Nodes is disabled per Material, Base Color and Color are not mirrored, i.e. not duplicates of one another, updating Base Color will not auto-update Color.