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What extension of mine are you referring to?

There is a "Disable on Components" option in the Modules Anywhere settings.
So you (or your users) could switch that on for com_gmapfp

The output of that com_gmapfp url contains {module} tags.
What do you expect to happen with those tags?

Leaving them as they are is probably not what you want, as that would output the raw {module} tags into the map.

So the question begs, should those {module} tags be used in the content used by com_gmapfp in the first place.
If not, tell the user that you can't use Modules Anywhere inside content used by com_gmapfp.
And/or strip the content from any plugin tags on your end of the code.

Or: parse the content through the system plugins before converting it to the syntax and final output you want.

Try disabling the "Fix HTML" option in the Modules Anywhere system plugin settings.

It is probably due to the system plugin ordering. Try changing the ordering of the plugins in question.
See: regularlabs.com/blog/242-plugin-order-is-important

Try disabling the 'Place Comment Tags' option in the Modules Anywhere system plugin settings.

It looks like the 'Place comment tags' option is not switched off yet. Or you should clear your cache.

All Modules Anywhere does is output the module content. If that generates newlines, then Gmapfp should handle those in its output.
I recommend you ask them to fix it on their side.
This is not a Modules Anywhere issue.

Try the new version.