There's "rep" and there's "reputation".
Your "rep" is an artificial numerical score that is entirely meaningless in the forums. Others have explained some of how it works, but whatever purpose it was once developed for it no longer serves at all because it is broken and abused heavily by an ever increasing number of people in the forums it seems. Perhaps that's even a good thing, because if it is abused heavily enough GOG might finally just remove the code and get rid of it completely as it only stands to divide the community more than anything these days. Best thing to do is ignore rep and just not care about it.
Your "reputation" on the other hand, that is something that others have little to no control over whether they like you or your posts or dislike you or your posts. Like in real life, your reputation is something each person decides in their mind about you based on their own personal observations of how you communicate, conduct yourself, and behave in the public forums, much like in the rest of real life.
The best thing to do is ignore rep, and simply try to be a friendly member of the community and contribute to the greater good. It's ok to share opinions, agree and disagree with others, but best to not take things too seriously or get overly heated in discussions etc. Overall the community here is a pretty friendly bunch of people. Even if you get caught up in a disagreement with someone, try to avoid making it a personal thing or holding grudges etc. and hopefully the other parties do the same thing and in the end everyone wins, and everyone's real world reputation grows in the minds of everyone else.
Nobody can doctor your "reputation" with a mouse click or browser addon, and anyone who has been around long enough here go by "reputation" not by "rep" when it comes to anything where either would matter. :)