Mongoose will allow you to SELL any work in PDF form that uses Mongoose Traveller 2nd edition rules and supplements, along with the content of ANY of Mongoose's Third Imperium products (regardless of whether it is for 1st edition or 2nd edition Mongoose Traveller).
In return Mongoose will require that
1) Mongoose/OBS will receive 50% of the sales price.
2) TAS have an EXCLUSIVE license to any original content you provide to use in the Traveller Aid Society. If Mongoose desired to use the content outside of the Traveller Aid Society then a separate agreement with the author(s) will be worked out.
3) That you allow anybody else in the Traveller Aid Society to use your original content
4) That you follow the guidelines for community standards.
Pretty much the exact same setup as the DM's Guild for DnD 5e, Forgotten Realms, and Ravenloft.
The way you should look at this is a mean for publishing Third Imperium material either systemless or using the Mongoose 2nd edition Traveller rules.
You should only use the Travellers Aid Program program if your product absolutely depends on being set in the Third Imperium outside of the Foreven Sector (which is covered by a separate license). Remember your alternative is Foreven, or negotiate a license with Marc Miller, or Mongoose.
Use the the Travellers Aid Program program if your product absolutely depends on being based on the 2nd Edition Mongoose Traveller rules.
In the above two cases the deal offered by Mongoose is a good one. Otherwise it is not.
Your alternative are to use
The Foreven Sector license and the Traveller SRD The Traveller SRD and no Third Imperium content. The Far Future Fair Use License (and release it non-commercially)
Negotiate a Third Party License.
Go through the submission process.
What innovative about the Traveller Aid Soceity, DMs Guild and the other programs is that the before there was a snowball chance in hell for anybody to use the IP of another company. Yeah there was the OGL, but beyond rules that OGL was rarely to applied to other interesting parts of RPGs, the settings. And even with rules some companies were never going to release a System Reference Document under an open license.
But now the Community Content is a intermediate step between the OGL and traditional licenses. In exclusive for losing control of your IP, and a hefty royalty cut to OBS and the IP Holder you get to near unrestricted use of that company's IP. And you get to do this without going through the formal negotiation process that license requires, or the oversight that a freelance contract gives.
It neither good nor bad but an option that now exists that didn't before.
For me I published OGL material for DnD. I would not normally use the corresponding DMS Guild program save for one exception; Greyhawk. If they incorporate Greyhawk as part of the DMs Guild then I have some work that I would publish there. It Greyhawk specific and would not work as part of any of the other stuff I make. So I have no problem with the conditions that the DMs Guild imposed on that IP.
The same with the Third Imperium. I have some science fiction stuff I created using the Traveller Rules that I will NOT be publishing in the Travellers Aid Society. But I also have some stuff that only make sense if set in the Third Imperium.
In end it is a series of tradeoffs, my recommendation is really think about it before you publish. But in the end if there is no other way, then do it. You will get 50% of your sale price and there is always the chance that will be well-received enough so that Mongoose will want to buy further rights to publish it outside of the TAS.
To me the Old School Renaissance is not about playing a particular set of rules in a particular way, the dungeon crawl. It is about going back to the roots of our hobby and seeing what we could do differently. What avenues were not explored because of the commercial and personal interests of the game designers of the time.
What are RPGs?
A game where the players play individual characters interacting with a setting with their actions adjudicated by a human referee.
Rules are an aide to help the referee adjudicate actions and to help the players interact with the setting.
Dice are used to inject uncertainty which make a tabletop RPG campaign more interesting than "Let's Pretend".
The only thing a player needs to do to roleplay a character is to act if he or she was really there in the setting in that situation.