First of all, a GFCI operates independently of other devices-it is not an overcurrent device, such as a fuse or breaker.
Dimmers for typical incandescent and halogen lighting devices operate by lowering the supplied voltage-they are variable resistors.
To properly diagnose this, I'd need to open the panel or fuseboard and use an inductive ammeter to see how much current is being drawn. When the circuit ampacity peak is being reached, the GFCI could be tripping due to a poor connection at any point on the circuit.
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