Both are run by Orthodox rabbis. Rabbi Ralbag is very well-respected in inyanei gittin, eruvin, geirus, etc.
Tablet K’s main issue is with gevinat akum. Rabbenu Tam allowed the consumption of cheese made with vegetarian rennet that was produced by goyim. (See Tosafot, Avodah Zarah 35b, s.v. chada). In modern times, so did Rav Soloveitchik and I’ve heard the same in the name of the Hazon Ish. Most poskim don’t hold like this heter when it comes to cheese, and we therefore require gevinat yisrael. Talmudic gezerot don’t change; cheese must be gevinat yisrael, just as we don’t clap on Shabbat or Yom Tov.
When it comes to hechsherim, the specific issues need to be looked at on their own merits.
Ashkenazim, per the Rema, traditionally aren’t makpid on halak/glatt. An Ashkenaz could eat HN hot dogs, theoretically. Glatt, however, is promoted as the normative standard for today’s Orthodox Jews. Almost everyone in kashrut would tell you that Triangle K is acceptable for things like frozen vegetables. Another hashash people have is with oil; cooking oil is transported in trucks that haven’t been thoroughly washed and is then used subsequently in Triangle K products.
Regarding Tablet K, it is noteworthy that the Conservative Rabbinical Assembly does not consider it recommended, and le ma’aseh, Avi Olitzky, a Conservative mashgiach in MN, says that he doesn’t hold by it.
At the end of the day, though, much of the kashrut politics are exactly that: politics.
If you understand and learn halakha as an organic, cohesive, unified whole, you better inderstand the reasons behind why people do the things they do. Before I started looking at halakha through a more alphabetic lens, I did eat Tablet K cheese, but I now believe that the heterim they use are incompatible with the actual halakha.