As an (Eastern) European, I thought that adding a somewhat different perspective might be potentially usefull.

From my perspective, this is may be a very serious offence.

Whenever someone tries to invade my private space, I first try to ask myself if that person really understands what is he/she doing.

In most cases they don't, so in my opinion the best way is to very slowly and clearly state something along the lines of: "Excuse me, but I consider this a private matter, please don't ask such questions in the future" <- it sounds very formal, and this is intentional. It makes people feel they are way out of line without actually hurting them the way open anger/sarcasm would.

On the other hand, in (rare) case of people who should know (because, for example, You informed them previously on this or similar matter) that they are crossing a line, I think that controlled cold outrage is the most justified reaction.
I stress controlled-cold, expressed preferably in situation when noone can overhear You (taking this person immediately into a different room is preferable), in half the usual volume of Your voice, cold intonation, very clear pronunciation and maintaining 100% direct eye to eye contact.
You want to controll Your choice of words in order to be perfectly clear and stay on completely objective grounds. Be excessively polite.
The objective is to state in no uncertain terms that such behaviour will not be tolerated and repeating this again will lead to a major conflict, but it has not - yet. It is always advisable to state very clearly and precisely what You consider a no-go ground and observe carefully in the future if the offender is actively trying to accommodate Your demands and be nice/not nice accordingly - particularly, expressing Your gratitude to people who try to understand and play nice with You is always a good idea. Carrots are better than sticks with most humans.

In general private space is that, private. In my eyes intentional violations of that space are an extremely grave offence. There is a reason why, for example, taking pictures of people without their consent is not just rude, its actually punishable by law in some EU countries.

Having said that, this particular question is typically dictated by positive attitude and feelings to You, and in general its a bad idea to make people feel bad for caring about You - thus, the option 1.

On the other hand if some people just refuse to understand, then You have to make them. Its always better to do this sooner rather than later, because the more You allow such people to stick their nose into Your life, the more they will push forward, and in extreme cases (which I have witnessed myself, unfortunately) this can lead to serious pathologies - especially when kids come into play.

In general, in life any problem is better solved earlier rather than later. Finally, as some other answers noted, You should coordinate with Your girlfriend so that You both present a united front - generally talking about everything important is, well, important in a relationship :)

As an (Eastern) European, I thought that adding a somewhat different perspective might be potentially useful.

From my perspective, this is may be a very serious offence.

Whenever someone tries to invade my private space, I first try to ask myself if that person really understands what is he/she doing.

In most cases they don't, so, in my opinion, the best way is to very slowly and clearly state something along the lines of: "Excuse me, but I consider this a private matter, please don't ask such questions in the future" <- it sounds very formal, and this is intentional. It makes people feel they are way out of line without actually hurting them the way open anger/sarcasm would.

On the other hand, in (rare) case of people who should know (because, for example, You informed them previously on this or similar matter) that they are crossing a line, I think that controlled cold outrage is the most justified reaction.
I stress controlled-cold, expressed preferably in situation when no one can overhear You (taking this person immediately into a different room is preferable), in half the usual volume of Your voice, cold intonation, very clear pronunciation and maintaining 100% direct eye to eye contact.
You want to control Your choice of words in order to be perfectly clear and stay on completely objective grounds. Be excessively polite.
The objective is to state in no uncertain terms that such behaviour will not be tolerated and repeating this again will lead to a major conflict, but it has not - yet. It is always advisable to state very clearly and precisely what You consider a no-go ground and observe carefully in the future if the offender is actively trying to accommodate Your demands and be nice/not nice accordingly - particularly, expressing Your gratitude to people who try to understand and play nice with You is always a good idea. Carrots are better than sticks with most humans.

In general private space is that, private. In my eyes intentional violations of that space are an extremely grave offence. There is a reason why, for example, taking pictures of people without their consent is not just rude, it's actually punishable by law in some EU countries.

Having said that, this particular question is typically dictated by positive attitude and feelings to You, and in general its a bad idea to make people feel bad for caring about You - thus, the option 1.

On the other hand if some people just refuse to understand, then You have to make them. Its always better to do this sooner rather than later, because the more You allow such people to stick their nose into Your life, the more they will push forward, and in extreme cases (which I have witnessed myself, unfortunately) this can lead to serious pathologies - especially when kids come into play.

In general, in life, any problem is better solved earlier rather than later. Finally, as some other answers noted, You should coordinate with Your girlfriend so that You both present a united front - generally talking about everything important is, well, important in a relationship :)