Didn't see a part number, but assuming this is a GPS or similar. The antenna is receive only.
Somehow on the board they have arranged that you can plug a receiving GPS antenna into either connector and the other, open one isn't an issue. I'd presume this is mostly by just keeping the line short, though it feasibly could have two inputs to the module.
Termination can be important? Absolutely: In RF even more so than audio. if transmitting or don't want reflections from open/shorted lines.
Summary:
Don't think we are in any transmitting situation, hence a lack of termination is not going to be an issue to the module safety.
The "other" connector is normally open, so removing it, carefully so as to not mess with the board too much, is likely just shortening the line a little, shortening a rather short stub off the line being used: used antenna connector to module.
Seems very likely to be ok.
Disclaimers: Never looked at how these modules provide the two inputs. Not an RF guy (even less than previously).
You could try asking UBlox.