Praise be to Allah.
The saheeh evidence indicates that it is haraam to listen to musical instruments, as has been explained in detail in the answer to question no. 5000. So it is not permissible to accompany nasheeds with any kind of music, or effects that imitate music, such as some rhythms that can be produced on the computer, which sound no different to music in making the listeners enjoy the sound and behave in a foolish manner; moreover using these rhythms is an imitation of evil and immoral people.
Shaykh al-Albaani (may Allaah have mercy on him) said: There may be another sin involved in that [i.e., nasheeds], which is that they may be performed in the manner of immoral songs and performed according to the rules of eastern or western music which makes the listeners enjoy it and makes them dance and behave in a foolish manner. So the aim becomes the tune and the enjoyment thereof, and not nasheed per se. This is a new error, and it is an imitation of the kuffaar and immoral people. That may lead to a further error, which is imitating them in turning away from the Qur’aan and forsaking it, and being included in the general meaning of the complaint of the Prophet (peace and blessings of Allaah be upon him), as Allaah says (interpretation of the meaning): “And the Messenger (Muhammad صلى الله عليه وسلم) will say: ‘O my Lord! Verily, my people deserted this Qur’aan (neither listened to it nor acted on its laws and teachings)’” [al-Furqaan 25:30]. End quote from Tahreem Alaat al-Tarb (p. 181).
It is well known that sharee’ah forbids listening to musical instruments because of the effect that their sound has on the heart, filling it with hypocrisy and making it turn away from the word of Allaah, so that it does not find any joy it except in these songs. And it is well known that some of these rhythms are more enjoyable than musical instruments, and their effect on the listener may be greater than the effect of musical instruments. So they are no less than them. It cannot be the case that sharee’ah would forbid one thing because of its evil effects then allow something that is similar to it or worse than it.
If the sound of these rhythms is like the sound of musical instruments, then they come under the same ruling as musical instruments and are haraam, and maybe more forbidden.
No exception is made from the prohibition of musical instruments except in the case of the daff (a kind of hand drum) only, in certain situations. That has been explained in the answer to question no. 20406.
If these rhythms are like the sound of the daff, then there is nothing wrong with listening to them in the situations in which it is permissible to listen to the daff.
And Allaah knows best.