This is overstated in my opinion and in my experience, particularly because the OP is inquiring specifically about UA and TG.

I do end-on-end separate ticketing all the time when going through BKK using UA and TG. I have had my bags checked through with no problem either way. Perhaps my ignorance is bliss, but I have simply bought my tickets in the most cost effective way, which is sometimes with an agent in BKK (this takes some doing, but can save a great deal), or the TG website. I never attempt buying TG flights on the UA website.

I don’t know the published policy, but I have done this several times to different destinations without problems or questions.

While on the topic, I’ve had seamless, trouble-free check-through of bags connecting either way between UA and SQ in SIN using separate end-on-end ticketing. I can say the same for connections in FRA between UA and LH.

On this count glex is absolutely correct. This is the risk that balances the benefit of lower cost. All the more reason to consider which airline and city-pair has a better on-time performance and allow extra time to be sure that your bags make the interline change. If you don’t make it for any reason, there can be some seriously high change fees. And glex is right about LCCs. If you don’t show up on time for Ryan Air or Wizz Air, you just donated to their cause.

Good advice about allowing extra time. Even with carriers agreeing to do interline transfer, it takes time. I once had a UA to LH transfer in FRA to ZRH (once again, with end-on-end ticketing). My bags didn’t make the change even though there was two hours between flights. You’d think that the timeliness of Germany would get bags heading for Switzerland out on time. But there was an extra security check at FRA, which the agents in ZRH told me happens all the time.