The effect you are describing can pretty much only be a content corruption effect. The Icon references are either wrong, or - more likely - the icon you are describing is the "unknown icon" error replacement. That however wouldn't cause bad links (choosing a promotion can't naturally lead to opening menus).
There are two places where content corruption can occur: With the mods or with the base game.

Detecting the source
Step 1: Remove all Mods from your mods directory (Documents > My Games > Civ 5 > MODS). Move them somewhere else, so you can restore the previous state in case of need. Step 2: Unsubscribe and resubscribe to Scout's Progress and Mod Test Helper.
Step 3: Launch a new game with both loaded (as late an era as you can), use the MTH building for extra EXP, then recruit a ranger and check his promotion state.

If Step 3 worked flawlessly, continue with Step 3 worked successfully, else continue with Step 3 did not work

Step 3 worked successfully
If this worked well, the Corruption is Mod-Based (thank god).
Step 4: Copy back all the other mods (do not write back SP, keep the new one; If Civ re-downloaded all already, this is a not necessary).
Step 5: Recreate step 3. If everything works, you are done. Otherwise continue with Step 6.
Step 6: Once again, remove the mods moving only some back (and if necessary unsubscribe from them for the duration, so they don't redownload). Then repeat step 3 to see whether it still works. Repeat Step 6 until you have found the offending mod (try starting with big and complex mods, they are most likely to be the culprit).
Step 7: When you find out which mod caused the problem in combination with Scout's Progress, try unsubscribing, deleting and resubscribing. If that works out well, you are done.
Step 8: The problem occurs with both SP and the other mod freshly resubscribed and downloaded. If that's the case, we have a clear incompatibility (and an extremely severe and unlikely one at that). Tell me which mod it was, I'll get right on fixing as fast as I can.

Step 3 did not work
Bad news: If a clean, sanitary mod installation still causes these weird events to occur (especially the menu redirection) then there is an extremely high probability that the culprit is in fact the game itself and you have corrupted game data. This can be corrected, but will likely require a reinstall of Civ 5 (Backup your saves first, to be on the safe side).

Important Note
I'm not an all-knowing developer. Error is possible, and I may well have forgotten an important aspect somewhere. If anything unexpected happens, please tell me (and tell me if your problem is resolved, that way it can be closed and I'll sleep better knowing everything's alright). If anybody out there has a better notion of the possible reasons or troubleshooting technique, tell me. I can never know enough :)

A little background on errors
Mods basically consist of 3 different kinds of elements:
- Information (Usually in the form of Xml)
- Logic (Usually in the form of lua)
- Resources (Icons, Images, models ...)
Information Level errors usually mean that merely some information is not there or fails to load (A promotion missing, a unit not there, that kind of thing).
Logic Level errors usually affect the way the game behaves more drastically. A menu might not work anymore, a button could call the wrong menu, all tiles might turn into desert at the beginning of a turn, that kind of thing.
I have yet to witness a Resource Level error. Theoretically, a corrupted image file might qualify as such.

Mod incompatibility most commonly occurs when several mods try to access the same Information block. For example, SP causes the Shoshone Civ-Ability to give all Scout units the ability to pick their goody hut upgrades. If another mod discards the Shoshone default Civ-Ability and instead gives them a new one, this will result in Shoshone scouts not receiving he ability to pick their goodies (but the rest of SP will still work).

Scout's Progress makeup
Scout's Progress however is completely and solely an Information based mod. It contains neither Logic nor Resources. The only Resources it uses are from the base game itself (It uses standard models, sounds, animations, Icons, etc.) that already existed in Vanilla Civ 5.
What this means is that while a part of Scout's Progress might fail to load (Mod-Incompatibility or corrupted files), it could never by itself cause the effects you described with choosing a promotion opening a menu (that's a Logic Level action).
Which is why I'm a bit perplexed by the error :)

I decided to go BNW, and after playing a full no-mod game, I tried MTH and SP. I had the weird icon mismatch in the first game, but all the scouting promotions were available. When I started another game everything worked fine and the sniper promotions were correctly available. Could I have had an older version of G&K? Is it possible to go back to G&K and try the sniper promotions again?

Alas, I know not how to go back to G&K and try again.
An old version of G&K is unlikely, at least if you're playing Civ 5 over Steam.

Maybe your issue is solved with this for good. If yes: Cheers. If it reoccurs however, we're likely back at the above debugging steps :(