I have a valve with IPS male fittings [https://www.amazon.com/Thermostatic-Mixing-Connections-Stepless-Adjustment/dp/B00SYC1IV6] [1] that I want to use with a couple of check valves [https://www.amazon.com/Camco-23303-Back-Flow-Preventer-Lead/dp/B000EDUTN6/ref=pd_sim_60_1?_encoding=UTF8&pd_rd_i=B000EDUTN6&pd_rd_r=7b50b42f-5a20-11e8-a532-1b8228080e91&pd_rd_w=U3Zcv&pd_rd_wg=LEeup&pf_rd_i=desktop-dp-sims&pf_rd_m=ATVPDKIKX0DER&pf_rd_p=7967298517161621930&pf_rd_r=5KFB32PEGQB2GTVA87C8&pf_rd_s=desktop-dp-sims&pf_rd_t=40701&psc=1&refRID=5KFB32PEGQB2GTVA87C8][2]. The first check valve I bought said it was compatible with the part, but the male connection for this part is NPTF. The IPS female thread on this check valve does thread about half way.
So I bought a female to female IPS check valve, but it won't thread more than one or two threads. I'm sure some PTFE and some gorilla power would do better, but I don't want to strip the valve. The threads on the valve almost seem to be tapered.
The final goal is to install the Thermostatic valve between the copper Hot and Cold supply lines, with an angle stop on the output of the valve.
Best Answer
IPS means Iron Pipe Size and references standard iron/steel pipe nominal inside diameter; "nominal" because it is actually the OD that is standardized. IPS pipe is commonly threaded to NPT (National Pipe Thread), which is indeed a tapered type thread. It seems to me that by your description all the pieces you have would have NPT. An "M" or "F" on a fitting would indicate male or female thread.
Thread quality can vary widely depending on a lot of things (technique, tool quality, tool maintenance, etc.). Knowing that the thread is tapered, I would go ahead and give it a bit of carefully applied muscle.
P.S.- please clarify your first paragraph because it is difficult to understand.