When the Aku Altar is around, be ready for a tough battle, as its mere presence puts a handicap on all Cat Units' levels depending on how much progress has been made in The Aku Realms as well as cancelling out + levels (see the linked article for more information) until the Mount Aku Invasion has been cleared. On its own, however, it does absolutely nothing to harm your units.
Due to this base's effect, what ends up mattering in its presence is units' stats when not skewed by + levels, meaning that Normal Cats, who often have more + levels than normal ones (20+90 being the max), end up massively underpowered, to the point of becoming useless. Similarly, Li'l Cats and Rare Cats tend to rely on + levels more than Super Rares, who tend to rely more on them than Ubers and no-gacha Cats. This results in cats of high rarity as well as drop rewards having a general advantage and being, therefore, recommended to use with priority (note that low priority doesn't mean anyone should be put on the side-lines, sometimes, if not often, stat-based Rares are still more than viable).
Aside from altering the unit balance, this altar also as an equalizing effect, allowing underleveled units to be used alongside high-level ones when the level cap is low.