If you have a 73mm BB shell you shouldn't need spacers under the cups. If the spindle is too short by approx 5mm, then the spacers are the culprit.

 

It could just be that the spindle is too short. Rival is traditionally a road groupset and the crank is probably designed to fit a 68mm BB. All the tech docs from SRAM for Rival 1 are all filed under "road".

 

Right, so Gravelbike says that the spacers should go out - but I am not sure...the bike store put the spacers in already traditionally, so one would assume that they know what they do and that the spacers are supposed to be in there. I know there is some confusion about whether spacers are supposed to be in or out with a 73mm BB GXP. So, in or out?

And RS VR6 says what I also heard from some other ppl - Rival's spindle is too short and only designed for road bikes. So, do all road bikes have 68mm BB?

 

Rival 1 is actually more towards CX, I put the shifter etc 11s group on my road bike because I wanted 1x11.

The answer is really simple:

Take a ruler, measure the bottom bracket housing. Likely it's 73mm. Bike shop was too stupid to measure and check first obviously. Remove the spacers, install the cranks and go ride.

Bottom brackets are mostly stated 68/73. Cranks may be different (road shorter than mountain). Road bike frames shouldn't have spacers in most cases.

And actually iirc my road bike which is a trek 1.2 is 68 but ultegra bb Sora crank, no spacers iirc.

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I took the Rotor 3D crank from my Cervelo S2 with a 68mm BB and tried it in my mountain bike with a 73mm BB. The spindle was too short. I thought I'd be able to swap spiders and run it on the MTB...no go. I also called Rotor and they told me the mountain crank has a longer spindle. The vast majority of road bikes are 68mm.

 

Ok, I measured again the bottom bracket housing, it is definitely 73mm, like stated earlier on.
I also took apart the bottom bracket. Now, there is a small black plastic distance tube between the two cups. With this black thing, you must use the two spacers on either side of the cups as otherwise there would be a gap between the cups and the bottom bracket housing. Now, I though I could leave out the black distance tube, as well as the spacers, then the crank would fit. But this is not the case either, the crank spindle is still too short.

Also, the when I check the bike components website from where I purchased the crank set (I bought the complete group set though) https://www.bike-components.de/de/SRAM/Rival-1-GXP-11-fach-Kurbelgarnitur-p43828/
it states only BSA 68mm for the bottom bracket, and not BSA 73. Does this mean that it only fits 68mm bottom bracket housings, or did they just forget to write down the BSA 73 measure because it is more typically used for road bikes/ cross bikes which pretty much always have a 68mm bottom bracket housing?

In other words, I guess I have answered my own question...the SRAM Rival crank set does not fit into a 73mm housing, no matter if spacers are left in or out.
Any additional comments/advice are appreciated.

 

The BB cups will thread into both 68 and 73mm shells. It's the spindle length that determines if the crank is road or mountain.

There is nothing much you can do. You need a crank with a longer spindle.