"If a Jewish baby is baptized, will she still be considered Jewish by the Jewish community? If not, will she later need to convert back to Judaism if she desires?"
If it is a real situation, turn to your Rabbi as protocol doesn't permit me to interfere in a Rabbi-congregant relationship. I am certain that your Rabbi has been through these kinds of issues before and will work with you.
If parents choose to baptize a baby, they have made a decision about the child's religious identity even if only for the moment. Otherwise, the parents could have chosen to wait to declare the child's religion or for the child to grow sufficiently old to declare their own identity.
There are some who say that if a baby is born to a Jewish mother, even if it is baptized, the baby is still Jewish and the parents are sinners for doing so.
However, to my mind this is a form of racism in religion. I prefer to believe that religious identity isn't something to which you are born; it is an identity or self-perception that is achieved through education, a home life, parental and grandparental influence, affiliation with a synagogue, the community, etc. It is my belief and practice to nonetheless convert" anyone who has been baptized but was born to a Jewish mother because most often they need a significant Jewish education if they are to function and be "at home" in the Jewish community.
For a child to be named in the synagogue or to have a ritual circumcision=brit milah, the Conservative movement requires that the child be born to a Jewish mother or be converted and then subsequently raised as a Jewish child in a Jewish home.
On the liberal side, the Reform movement which recognizes religious identity from either Jewish father or mother, has determined that the child is Jewish ONLY if it is raised uniquely in the Jewish tradition; baptism would not be acceptable, even if the child were to be named or have a ritual circumcision (brit milah).
Traditionally, it is also customary to allow the child if converted as an infant to be given the opportunity to truly choose whether they wish to remain a member of the Jewish People. Judaism believed that it would be morally wrong to take advantage of a child's vulnerability and commit them to a Jewish identity without any choice, ever.
My own approach was to speak with the young person a number of times around the event of Bar and Bat Mitzvah, in addition to teaching them in a group class. I would raise to them at one time or another, if they had a choice, would they still choose to be a Jewish. I never once had a child say no - but then they were about to celebrate Bar or Bat Mitzvah, public recognition of their accomplishments and new status and receive presents and often have a big party. (Who really would say no under those conditions?)
Realistically, if later as an adult one wished to exercise the right of denying one's Jewish identity, clearly they could do so.
This is a very technical issue, as you can see, and I urge you to speak with a community Rabbi. If there isn't one, let me know where you live and I'll find the closest Rabbi to your community.
Rabbi Barry Dov Lerner