Why I Disagree
"Rinne Sharingan: The Kekkei Mōra dōjutsu that is the progenitor of both the Rinnegan and the Sharingan. It gives the user the basic abilities of the Sharingan and allows the user to cast the Infinite Tsukuyomi, a genjutsu which can affect the entire populace of a planet."
This is a Quote taken from the Naruto Wiki, the problem with this is that the premise relies on her performing any of the Rinnegan abilities in their fight, it's not a statement made in Verse or by a credible source. this doesn't disprove that she can't use these abilities but makes an Observations based on what we have seen in their limited fight and using it as a proof is the same as saying she can't use these abilities because she didn't show them in her fight and using it as a supplementary source for the first argument would lead to Circular Reasoning.
There's also the fact that the assumption is that it must be true but this is an Appeal to Authority and an Authority ill question and in due part because the structure and intention of the Naruto Wiki is not the same as ours.
Essentially the Negative comes down to Kaguya not showcasing her abilities, therefore, she must not have them, it's a fine assumption to make but I disagree.
Here's Why.
The Rinnegan is an advanced version and the predecessor to the Sharingan, the Rinnegan has literally all of the innate Sharingan abilities and more, with the exception of specific abilities that are exclusive to certain users. now the Rinne Sharingan is to the Rinnegan what the Rinnegan was to the original Sharingan, the original eye "power" which every other eye power has deviated from including the Byakugan. for us to assume that the Rinne Sharingan doesn't possess the basic innate abilities that are granted by its inferior deluded version would be us assuming that the RinneSharingan is somehow an exception to a consistent pre-established chain of evolution that has consistently shown us that their predecessors are capable of the same stuff but more, which would require us to make even more assumptions.
There's also the fact that Sasuke Outright Refers to Kaguya's Genjutsu as Rinnegan Jutsu.
as seen
Here
The Name
It's a Combination of the word Sharingan and Rinnegan.
It Possesses both Tomoe of the Sharingan and the Ripple Pattern that's exclusive to the Rinnegan.
Then we have External Sources outside of the canon that is generally consistent with this assumption such as Kaguya using the Almighty Push and in fact, it's very likely that she used the Almighty Push in the manga against Naruto.
basically, both parties require there to be assumptions, however, the Pro Rinngan requires far less as it doesn't contradict established lore and has enough supplementary proof to imply the positive.
abductive reasoning and Occam's Razor will do the rest. while the Anti Rinnegan entirely relies on one situational event and for us to ignore context..