I haven't found a good answer for this anywhere yet, so I'm just gonna ask here. Is it unacceptable for a Jew to not keep shabbat, even if they are trying to become observant slowly and don't know all the shabbat laws yet?
There are halachic sources for a step-by-step approach, and halachic sources for an all-and-not-nothing approach. This is a summary of the first chapter of "After the Return" (Feldheim 1994), "Evolution or Revolution?" by Mordechai Becher and Moshe Newman and it is highly recommended reading for people in the position as outlined in the OP.
There He placed before him statutes and judgements... (Shemot 15:25)
Chazal (cf. Sanhedrin 56b; Onkelos, Mechilta, Midrash Rabba ad loc.) explain that Hashem gave some mitzvot before the giving of the Torah. The Ramban explaining Rashi and R Shimshon Rafael Hirsch explain this was to acclimatize the Jewish people to doing mitzvot. Hagaon HaRav Moshe Shapiro zt'l explains that this can be used as the basis for an approach to someone new to Torah and mitzvot.
Hagaon HaRav Moshe Sternbuch shlita in his responsa Teshuvot V'hanhagot on OC 350 explains that one should follow the order of a child learning Torah and mitzvot in chinuch. Kashrut would be considered priority over Shabbat observance, for example. Wisdom should be used to measure the level of interest, the level of emunah, the capabilities and passion in the prospective baal teshuva to guide the process. The point is he says specifically that there is no reason to start with Shabbat.
A person should also try to know himself as he will be the main guide of his own process. If he feels that he would be overwhelmed then according to these opinions he shouldn't go from 0-613, as this will end up with him forsaking Torah and that would be far worse. To commit a minor sin to prevent one committing a larger sin is an obligation! See Shabbat 4a, Tosafot and Meiri ad loc.
Other sources for gradual introduction to mitzvot:
- Pitchei Teshuva 10 on SA YD 268:12 quoting the Responsum of Rashbash 68 discussing the return process of apostates.
- Ibn Ezra on Hoshea 14:2 "return little by little", see also Beit Elohim of Rav Yosef M'trani (Sha'ar Hateshuva 1)
- Netivot Olam, Netiv Ha-Teshuva Ch 6 of Maharal explains that Hashem accepts partial repentance (based on chiddushim on the sugya in Shevuot 39a God "removes the guilt of those who repent and does not remove the guilt of those who do not repent")
To address the point of hypocracy, the Rambam writes in Hilchot Teshuva 7:7 that one who does mitzvot while also doing aveirot (sins) has the reward for his mitzvot torn up in front of him. Kabbalistically as well, according to Zohar and the writings of the Ari, it states that when a rasha (sinner) does a mitzva, it actually gives power to the forces of impurity (although this would not apply to a tinok shenishba, someone raised without a proper education for Torah and mitzvot, which probably applies to everyone nowadays - see The Tinok Shenishbah written by Rabbi Chaim Rapoport for the London Beth Din in 5757).
It seems there are many answers to argue against the "Revolution" approach, starting with Rambam himself who rules (Hilchot Netiyat Kapayim 15:6) that a Kohen who does certain sins is still obligated in Birkat Kohanim (the priestly blessing) and says "we do not tell a sinner to add evil and not perform mitzvot", a clear contradiction. See also his Iggeret Ha-Shemad where he encourages people to draw sinners to Torah and mitzvot.
- The Chida states that if a rasha does a mitzva with complete devotion, he is rewarded (quoted by Rav Yaakov Hillel shlita in an unpublished responsum)
- Rav Moshe Shapiro explains that this does not apply to someone who is trying to connect with Torah and mitzvot.
- Rav Sternbuch explains in Haderech Leteshuva 7:7 that when the rasha completes the teshuva process, the reward for the mitzvot will be retroactively reclaimed, so we should encourage people in the process to do mitzvot even if they aren't doing all of them yet.
- Rav Hillel explains in the aforementioned responsum that the negative effects of not doing mitzvot is worse than doing them in the state of being a rasha
- HaRav Yosef Cohen in Sefer Hateshuva 7:7 explains that the reward being torn up just means it will not be provided in Olam Haba (the afterlife), but it will be rewarded in this life.
All of these authorities show that one should do mitzvot even if one is violating other mitzvot.
The next chapter in the book is priorities in mitzvot. Overall, it concludes that if one is not inspired yet, he should focus on positive mitzvot, but if he is ready to accept the yoke of halacha, he should focus on negative mitzvot. When it comes to positive mitzvot, one should probably start with Torah study, and then mitzvot that help him feel part of the community, and then kashrut.
There is much depth there so I recommend purchasing the sefer (or reading it on google books here) and reading the whole chapter.
Important note: nobody should do anything based on a book or this answer alone. One should always seek the guidance of a Rabbi to get to know him personally and walk him through the process. CYLOR!