Is it permissible to perform ablution (wudu') and ritual bathing (ghusl) while there are remnants of "acrylic" on the nails, if removing it completely might cause damage or injury to the nail?

The visible part of the nail is among what must be washed during Wudu (ablution) and Ghusl (definition) (ritual bath). Any barrier on it that prevents water from reaching it must be removed. So, if one leaves even a small part of what must be purified, their purification is not valid. However, if the trace is very slight, or its removal is impossible without causing harm, then it is hoped that there there is no impediment to purification with its presence, while striving to remove it in a way that causes no harm.