Obliquity anything from 11 - 28 degree swings which would obviously
affect seasonal changes. Is this a fact (where's the evidence) or
I don't like to use the word fact in a situation like this. What that variation is, is a mathematical model based on well understood but pretty complicated n-body gravitational perturbations between planets, so, it's likely accurate. Whether it's a fact is perhaps a matter of semantics, but I don't like to use the word fact in this situation.
That said, it's very likely true that Mars undergoes both significant axial tilt changes and eccentricity changes over thousands or tens of thousand year cycles, and if variations like that happened on Earth, they would cause havoc to our climate.
Everything else being equal, that kind of variation should generate considerable glacial movement on Mars' poles, but everything isn't equal between Mars and Earth.
Ice ages on Earth require large land masses on or near one or both poles, where ice can build. Glaciers can't form in open deep ocean water, they require land, where the summers are cold enough that ice can build up, which, over thousands of years of buildup, becomes a glacier.
Mars lacks the water to expand it's glaciers. Nearly all Martian water is either underground or already frozen on it's North pole, so there's no water to add. Literally about 99.99999% of Mars' surface water is already part of one of it's two glaciers on it's North & South poles.
Unlike Earth - where there's always some water in the atmosphere and there's always the possibility of snowfall, so Earth's glaciers can always grow bigger if the seasonal temperature allows it. Mars has no ice to add to it's glaciers.
That limits Mars' glacial expansion to CO2, and that does happen to a degree. Mars glaciers do add CO2 during the winter and return it during the summer, but that's seasonal and Mars has only so much CO2, so it's glaciers could only expand as far as it's atmosphere would allow.
Mars' atmosphere is about 2.5 x 10^16 kg. Mars' surface area is about 1.4 x 10^14th square meters, which means it's entire atmosphere works out to about 180 kg per square meter, which would be about 7 inches high if frozen into dry ice. 7 inches means that Mars can't form glaciers like Earth can, no matter what it's axial tilt or eccentricity variation. It lacks the material.
If things were very different on Mars, like, lets say it had ammonia-water oceans and a thicker atmosphere and regular snow and rivers, then it might undergo glaciation periods and ice ages comparable or perhaps exceeding Earth, but it can't do that because it lacks sufficient atmospheric material.
Mars can create a thin ice cover and it can do that seasonally:
Mars' seasonal ice, winter to summer, is prone to considerable adjustment.
And, I don't want to say 100% that Mars undergoes no glacial changes. It still might, as it goes through it's Milankovich cycles. I'm not sure anyone knows for sure what Mars' ice caps looked like 10,000 or 100,000 years ago, so it's possible there were noticeable changes, but Mars' still lacks the material to form new enormous glaciers the way Earth can.
As a sidebar, and perhaps this could be looked into in more detail in a separate question, but Mars may undergo some kind of below the surface glaciation. Posting article as a curious sidebar only.