This is actually rather complicated. I am Jewish and I was born to a Jewish parents (my father actually studied to be a Rabbi and I am studying to be a Rabbi) so I study this stuff.
If you convert via an Orthodox conversion you are to be seen as every bit as Jewish as someone who was born to Jewish parents minus the fact that a Kohen cannot marry a female convert.
Now, that said, there are some who do look down on converts even though halacha says we are not to do that. Yes these people do exist but they tend to be much older and they tend to be very self righteous and rather arrogant to begin with. On the the flip side, there are people like my family, who hold converts in a little higher esteem than those of us born Jewish because they have chosen to take on Jewish law and Jewish obligations when they did not have to. They have chosen to be a part of the Jewish people knowing that means a very different life than they were used to and knowing it can and probably at some point will mean discrimination and persecution.
So, yes, there is discrimination but it is no the norm in the least. I would assume there are people in other faiths who might look down on converts as well because bigotry exist across the human spectrum and Jews are not immune.
What you do get more of are Orthodox Jews who are somewhat hostile to Reform Jews (born or convert) because they do not see them fulfilling halacha. This is also not that common (most just worry about themselves and their family) but it too does happen.
I think most people, at least from my experience, who convert to Orthodox Judaism, they are accepted (by the community) long before the conversion process is actually complete. They attend Shul and thought are not counting in a Minyan, they often attend Shul in the morning, afternoon and evening. They live as a Jew (and for a male that is rather obvious as you wear a kippah, tzitzit, etc that "marks" you as a Jew beyond all doubt). Some people do not want males to wear tzitzit before the conversion is complete and others say they should but regardless. My family and most of the people I know hold converts in a little higher esteem but yes, you may meet someone who looks down on converts but they are going against Jewish law.