Update based on OP's link to Sole F85 manual:
I'm a little concerned as the manual refers to 110V. That has not been the standard for decades, which indicates a misunderstanding of the US electrical system. I can't blame it on this being an old product as the Sole web site lists all kinds of advanced features such as WiFi, which simply did not exist in the 110V days. That may point to a misunderstanding of electrical appliance design and a blanket GFCI prohibition that is based on the first generation of GFCI together with older treadmills and not necessarily applicable today.
That being said, the normal rule is that, particularly for a UL or ETL or similar listed device (is this UL listed?), you follow manufacturer directions.
The treadmill only needs a 15A circuit. However, it also raises the issue of high current requirements at startup and possibly other times. So that points to a dedicated (no spare capacity for other stuff) 20A (gives you more capacity) circuit. The GFCI prohibition (which, to me, is ludicrous) forces you into a single receptacle, instead of the usual duplex, to help with any inspection/permitting issues. Label it "treadmill only, not GFCI protected". Since it will be the only receptacle on the circuit, you must use a 20A NEMA 5-20 instead of the usual 15A NEMA 5-15 (a duplex 5-15 is allowed on a 20A circuit, but not a single 5-15).
Below are general rules for any plug-in exercise equipment.
Dedicated circuit depends on instructions for the particular treadmill. May say any 15A or 20A, any 20A, dedicated 15A or 20A or dedicated 20A. Impossible to guess.
Install on GFCI per code. Can be GFCI/breaker or GFCI/receptacle.
A well designed new device should not to GFCI unless a fault occurs. Newer GFCI should also be more reliable than older ones. Get the treadmill. Install properly. Come back here if you get frequent nuisance trips.
The exception for refrigerators is a cost benefit analysis (potential for spoiled good being a key factor). The factors for a treadmill are quite different.