Is a Jew allowed to marry another Jew who is generally unconcerned with observing Judaism?
On one hand, the first Jew's observance could be negatively affected by the second Jew's non-observance, and there could be other complications in the marriage if there are differing observance levels. On the other hand, marrying another Jew ensures that the non-observant Jew won't marry a non-Jew and produce non-Jewish or assimilated Jewish descendants.
As cited above, the Shulchan Aruch advises against it. The Mishna in Kesubos talks about divorce if it's discovered that a spouse is non-observant, and/or the non-observance is affecting the observant spouse. (More on that in a moment.)
Let's start with two important points here:
Never go into a marriage thinking "I am saving this person from something worse."
Never go into a marriage thinking "I am going to change this person."
(Let's also remember the Gemara says don't go into a marriage that is likely to lead to resentment; "love your neighbor like yourself" applies to your spouse too.)
Rabbi Mordechai Willig shlit"a has a YUTorah mp3 on Kibud Av V'em where he addresses the obligation of respect (broadly) towards a non-observant parent. In the course of that, he remarks: Chazal also say you have to respect your spouse. Today it would be scandalous, but not long ago it was not uncommon -- suppose one spouse is observant and the other isn't; does that mean he doesn't have to respect her (or vice versa?)
The really big questions that will need to be asked are how the kids will be raised, and what about things that affect the other spouse -- most notably "family purity" and "is the food in our kitchen kosher?" (This can get a drop trickier when we address the question of "can I trust a person who doesn't keep kosher to keep my plates kosher?")
Long story short: it's generally not the greatest idea, but with a lot of agreement and planning, it could be doable. There doesn't seem to be a clear thou-shalt-not against it. The least-problematic scenario would be something like a second marriage in which the kids are out of the house and Nida is no longer a biological concern.
This is the Halacha in the Shulchan Aruch Even Haezer 2,6
לעולם ישתדל אדם לישא בת תלמיד חכם ולהשיא בתו לתלמיד חכם. לא מצא בת תלמיד חכם, ישא בת גדולי הדור. לא מצא בת גדולי הדור, ישא בת ראשי כנסיות. לא מצא בת ראשי כנסיות, ישא בת גבאי צדקה. לא מצא בת גבאי צדקה, ישא בת מלמדי תינוקות, ואל ישיא בתו לעם הארץ:
הגה: ועל בנותיהן הוא אומר: ארור שוכב עם בהמה. וכל זה בעם הארץ שאינו מדקדק במצוות
Basically there is a whole list of preferred Jewish girls and it is seriously not recommended to marry a woman from a non orthodox background who acts like her background (it is not in your power to change someone as they were given free will) unless of course she now keeps the Mitzvot in which case it is perfectly fine.*
*ולא בכל עם הארץ אלא במי שהוא חשוד לעבור
The Tur Beit Yosef says that this only applies to those who are suspect to transgressing Mitzvot.
Anyone can achieve a return or teshuva to G-'s holy name. With that I'm mind, it's not advisable to marry someone secular, as that return to HK"B has not happened yet.
