Although holding mourning sessions and gatherings for Imam Husein (as) and his companions is a great act that brings one massive blessings and rewards, yet if these gatherings are used to strengthen and propagate false teachings that contradict true Islamic beliefs taught to us by the imams, not only will attending them not draw any blessings, it will most probably entail the anger of Allah (swt) as well.
Your question suggests that you have no doubt in the falsehood and untruth regarding the beliefs of the group you mentioned, and that your question is only about attending "religious" majalis [gatherings] that they hold. Therefore, we will not address the fact that this group is a totally false and misguided one who has strayed from the right path, and will only discuss interacting with and accompanying them:
Our leader, Imam Ali (as) was a unique and irreplaceable character who was deprived of his clear right by those who totally hated and despised him. Others, who seemed to be his advocates and friends at first sight, exceeded the bounds and called him God; according to Imam Ali (as), both groups are in ruin.
We the followers of Imam Ali (as), have to put his orders to practice; one of them being to at least show a frowning face to those who believe in Imam Ali (as) being deity.
Naturally, when one attends ceremonies held by these individuals, he/she has to greet and show respect to them, and this contradicts what the imam has ordered us to do regarding them. Imam Ali (as) says: “One who goes to the one who does bid’ah (innovation in religion) and shows him respect has in a way helped destroy Islam from the roots.”
“What if one goes to these ceremonies without showing the host any respect?” you may ask. The answer is that in such a case, the hadith of Imam Sadiq (as) applies that says: “Neither speak nor sit with them [those who are innovators in religion], so that others won't think that you are one of them.”
Not all people will be aware of the fact that you aren’t one of them and that you're just there to support the movement and sacraments of Imam Husein (as), they will perceive that you are one of them and such will result in their lot being strengthened. Imam Sadiq (as) says: “It is not good for the believers to be present in sinful gatherings in which they can in no way change.” Anyway, being with these people and having any relationships with them might result in the anger of Allah (swt) covering all of those present with them, even though they have inner hate for their false acts. In a hadith we read:
“One by the name of Ja’fari narrates that Imam Ridha (as) told him: Why is it that I sometimes see you with Abdul-Rahman, the son of Ya’qub?! I replied that he is my uncle! The imam answered that he has false beliefs regarding Allah (swt)! If you want to continue to accompany him, then no longer come to us, and if you like to continue being with us, no longer go to him! I said: He can say whatever he likes, I don’t share and confirm his beliefs, so how will I be sinning by just sitting with him?! The imam replied: Don’t you fear that if he is to be punished, you will also suffer by his punishment?! Have you not heard the story of Prophet Musa’s (pbuh) companion whose father was in the army of the Pharoah; he left prophet Musa (pbuh) to advise and guide his father when the army was in pursuit of Bani Isra’il! He was busy advising his father in the army of the Pharoah when all of a sudden Allah’s (swt) punishment arrived and he and his father along with the army of the Pharoah all drowned. Prophet Musa (pbuh) heard of this incident and said: “Although the son is now in the grace of Allah (swt), nevertheless, when Allah’s (swt) punishment arrives, even the good who are next to the sinners will not be immune!”
The abovementioned individual was on the right side during the clash of good and bad, yet since the time for advice had past and when he was in the middle of the Pharoah’s army, he was counted as one of them, he suffered from their worldly punishment and drowned in the sea. We can conclude from this hadith that even though before becoming aware of these hadiths and how the imams want us to interact with these people, and also even though we would attend these ceremonies with pure intentions, and inshallah will be rewarded because of these pure intentions, yet if anything causes us to be part of the lot who have gone astray, there are chances that we will also suffer from their punishment; a punishment that will have a true impact on our lives.
In closing, we will mention one more point from the Quran that has to do with your question:
Although the Hajj rituals that the mushriks would perform were very similar to those the Muslims performed, yet Allah (swt) prohibited them from nearing the Ka’bah and performing the Hajj rituals by revealing a verse on this matter! The reason behind this prohibition can be because the misguided shouldn’t be free to even perform correct religious sacraments, for they can even take advantage of this situation for spreading their false beliefs!
The same goes for your question as well, and although our imams have stressed on the issue of upholding the slogans and supporting the movement of Ashura time and time again, these ceremonies shouldn’t become an instrument for the spread of false beliefs, therefore, attending such ceremonies aren’t encouraged at all.
Of course, all that was said applies when you have no effect on these people, but assuming that you want to sit with them in order to enjoin good and forbid evil when all the conditions are met for such a thing, it might even become wajib to do so.
 If you have any doubt regarding this subject, you can query about it in a separate question from this site.
 Nahjul-Balaghah, pg.489, Short Sayings, saying no. 117.
 Muhammad ibn Hasan Hurr Ameli, Wasa’ilul-Shia, vol.16, pg.143, hadith 21194.
 Ibid, vol.16, pp. 267-268, hadith 21533.
 Ibid, vol. 12, pg.48, hadith 15610.
 Ibid, vol.16, pg.260, hadith 21512.
 Ibid, vol.16, pp.260-261, hadith 21513.
 Tawdihul-Masa’el (annotated by Imam Khomeini), vol. 2, pp.756-758.
 Tawdihul-Masa’el (annotated by Imam Khomeini), vol. 2, pp. 756, issues 2786, 2787, 2788, 2789.