My new garage opener trips GFI
The answer to this is a wee bit complicated.

The Genie Excelerator II uses a DC motor and an electronic adjustable speed drive (ASD) to open a garage door quickly.   If you look at the “Operation and Maintenance” manual, you will see a slightly ominous note in “General Troubleshooting – Opener does not run”  that reads, “[Check for] a non-compatible GFCI.  NOTE:  A licensed electrician must replace non-compatible GFCI’s.”  They do not say why the note is there.

It turns out that GFCI’s are frequency sensitive and an ASD produces high frequency harmonics that are electronically generated.  If the ASD happens to generate harmonics in the GCFI’s sensitive area, then bingo, the ASD and the GFCI are not compatible.

Here’s a link to a helpful technical paper on the topic:

http://www.jonathankimball.com/pdf/gfci_ecce.pdf

In commercial and industrial environments, appropriately sized inductors called “line reactors” are installed upstream and/or downstream of an ASD to filter harmonics that would otherwise cause electrical problems.   In a residential setting I imagine such a measure is not worth it.  The implication of the language in the Genie manual is there are GFCIs for homeowners on the market that contain internal filtering to mitigate the ASD compatibility problem.

EDIT:  The specifications for GFCIs tolerant of ASD loads should indicate they are a "high harmonics" type.