Being born a Jew is pretty simple. If your mother is Jewish then so are you, if she isnt then neither are you. It doesnt matter whether your father is Jewish or not.
Conversion is much more complicated. Judaism does not actively encourage conversion, in fact, it discourages it. Discouraging conversion helps to filter out those lacking the proper degree of committment.
Once someone has converted to Judaism they have the full status of Jews. They are Jews in every way, and, just like any other Jew, they can never cease to be Jews.
The Torah says it is a special mitzva to love and to be kind to converts even more than to ordinary Jews. Also, it is a mitzva not to be unkind to a convert.
You shall love the convert, for you were strangers in the land of Egypt.
Devarim (Deuteronomy) 10:19
Do not hurt the feelings of a convert or oppress him, for you were strangers in the land of Egypt.
Shemot (Exodus) 22:20
Do not oppress a convert, you know how it feels to be a stranger because you were strangers in the land of Egypt.
Shemot (Exodus) 23:9
When a convert comes to live in your land, do not hurt his feelings. The convert should be to you exactly like a born Jew and you
shall love him like yourself, for you were strangers in Egypt - I am HaShem, your G-d.
VaYikra (Leviticus) 19:33-34
This has been established since the earliest days of Judaism. In the Torah, there are many references to "the strangers who dwell among you" or "righteous proselytes" or "righteous strangers." These are various classifications of non-Jews who lived among Jews, adopting some or all of the beliefs and practices of Judaism without going through the formal process of conversion and becoming Jews. Once a person has converted to Judaism, he is not referred to by any special term, he is as much a Jew as anyone born Jewish.
Nevertheless, a conversion not performed according to Jewish Law, as described in the Torah, is not valid. Although anybody can become Jewish, a Jew cannot become something else. Even if a Jew lowers himself/herself to practice other religions, he/she is still Jewish and will be judged (and punished) like a Jew, in the World to Come.
The Jewish People are all responsible for one another. It is the responsibility and the obligation of every single Jew to learn Torah, and to teach Torah to other Jews. Every Jew should make time to learn Torah, should live in a community where he can live according to the Torah, and should carefully select a good Jewish school for his/her children, to provide them with the best possible Jewish education.
The Jewish Nation must always be united as One People, with One Torah, and One Land. We have a common destiny. Political differences of opinion should never divide us. As our great Torah sages and true Jewish leaders say, "That which unites us is far greater than that which divides us."