BaseCamp should ignore extensions in gpx files that it doesn't know how to handle

BaseCamp already does ignore unknown extensions. However, when you want to add your own extension you also need to add a reference to a schema that defines the extension, otherwise the file is not valid. BaseCamp is very strict regarding validness (every program working with XML data should be), but luckily for you it doesn't actually check the schema. So you don't have to create one yourself, and something like this would suffice:

[html]
<?xml version="1.0"?>
<gpx xmlns="www.topografix.com/.../1" xmlns:xsi="www.w3.org/.../XMLSchema-instance" xmlns:myext="www.markcusd.com/.../v1" creator="Garmin Desktop App" version="1.1" xsi:schemaLocation="www.topografix.com/.../1 www.topografix.com/.../gpx.xsd www.markcusd.com/.../v1 www.markcusd.com/.../WaypointExtensionv1.xsd">
<wpt lat="38.865943" lon="-77.673446">
<ele>134.26989827957</ele>
<name>Waypoint1</name>
<extensions>
<myext:AExtension>
<myext:WayptData>some extra info</myext:WayptData>
</myext:AExtension>
</extensions>
</wpt>
</gpx>
[/html]

Note that when you export the waypoint from BaseCamp your custom extension will be lost. BaseCamp uses a different format to save data internally, and it saves only the stuff it knows.