It does look like a fabulous club and great good fun. If this club and its members help preserve open land to ride on, then bravo and good for them.
You keep saying “we are not in the UK” but what you’re missing is that this is the Chronicle of the Freakin’ Horse, pretty much the authority/major outlet on foxhunting in the US and headquartered smack dab in the middle of Virginia Hunt Country. So it is understandable that people are taking offense to your calling your club’s activities foxhunting. Because they know from foxhunting.
That doesn’t mean that your club isn’t wonderful, and isn’t providing a great opportunity for people to learn to ride cross country in a group setting and that you shouldn’t continue to have a blast.
But more than understanding terminology (there’s no “hunt master”; there’s a huntsman, an MFH and/or field master) or turnout (no square pads, no bright colors, no boots or polos), you need to know that an actual hunt club actually hunting would never lark over fences that there was a way to go around. It’s actually considered rude. You jump because you need to get from point A to point B, usually panels or coops set in pasture fences. Nothing in standards, nothing in jump cups, nothing preset.
So call it mock hunting, call it a hunt trail ride, call it lots of fun. But don’t get upset when people tell you not to call it fox hunting.