How to reproduce:
1. Open user's attached 'Bug.zip' project
2. Open 'SampleScene' Scene
3. Zoom out the viewport to clearly see that 'QuadWithConnectedNodes' GameObject does not receive fog
4. Open 'ParticleUnlitWithConnectedNodes.shadergraph'
5. Connect Position Node Port to Unlit Master's Node Alpha Port and save Shader Graph
6. Notice that 'QuadWithConnectedNodes' GameObject receives fog

Expected result: GameObject receives Fog regardless Position Node connected to Unlit Master's Node Alpha Port if Surface Type is set to Transparent
Actual result: GameObject does not receive Fog when Position Node Port is connected to Unlit Master's Node Alpha Port and Surface Type is set to Transparent

Reproducible with: 2019.3.0f2(7.1.1, 7.1.5, 7.1.6), 2020.1.0a16(7.1.1, 7.1.5, 7.1.6)
Could not test: 2017.4.35f1 HDRP is not introduced, 2018.4.14f1 Package Manager is not introduced, 2019.2.16f1 due to HDRP errors and Shader Graph serialization errors

Notes:
1. Video of reproduction attached in Edit
2. Reproducible on macOS and Windows also macOS and Windows players
3. Reproducible with other nodes too (for example Scene Depth)
4. Could not reproduce with Surface Type Opaque