Praise be to Allah.
With regard to the Mawlid and whether the one who does that is considered to be a Muslim, you will find a detailed answer in the Seasonal topics section of this website. In brief, those who do this are of many kinds, depending on what they do – although the Mawlid is in and of itself bid’ah (an innovation). But the ruling on those who do it depends on what actions contrary to sharee’ah they do in this Mawlid. Therefore the matter may extend as far as shirk and going beyond the pale of Islam, if any actions which are known to constitute kufr are committed on this occasion, such as calling upon anyone other than Allaah, or attributing any divine qualities to the Prophet peace and blessings of Allaah be upon him) etc. But if it does not go that far, then the one who attends such events is a faasiq (rebellious evildoer) but not a kaafir, and his fisq (rebellion) varies according to the unIslamic or innovated actions he does in the Mawlid.
With regard to the issue of marrying a man who participates in things like the Mawlid, the ruling varies according to the state of the man. If he does things that constitute kufr then it is not permissible to marry him under any circumstances, because Allaah says (interpretation of the meaning):
“And give not (your daughters) in marriage to Al-Mushrikoon till they believe (in Allaah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater), even though he pleases you”
Such a marriage would be regarded as null and void, according to the consensus of the scholars.
But if the innovation does not reach the degree of kufr, the scholars still issued a stern warning against marrying innovators. Imaam Maalik (may Allaah have mercy on him) said: “Do not marry a woman from among the innovators, or give your daughter in marriage to an innovator, or greet them with salaam…” (al-Mudawwanah, 1/84). Imaam Ahmad (may Allaah have mercy on him) said something similar.
The four Imaams (may Allaah have mercy on them) stated that religious compatibility between the man and woman is one of the matters which must be taken into consideration. A faasiq (rebellious evildoer) is not compatible with a righteous, religiously-committed Muslim woman, because Allaah says (interpretation of the meaning):
“Is then he who is a believer like him who is a Faasiq (disbeliever and disobedient to Allaah)? Not equal are they”
Undoubtedly, following innovation in religion is one of the most serious forms of fisq (rebellion, evildoing). Paying attention to religious compatibility means that if the woman discovers that her husband is a faasiq, or if it becomes clear to her guardians that the husband is a faasiq after the marriage contract has taken place, then the woman or her guardians has the right to object to this contract and ask for it to be annulled. But if they choose to forego this right, then the contract is valid.
Hence we should be careful to avoid such marriages, especially since the man is in charge of the woman (qawwaamah) and he may give the woman a hard time or force her to commit some acts of bid’ah, or make her go against the Sunnah in some matters. With regard to the children, their situation is more serious, because there is the risk that he will bring them up to follow his innovation, so they will grow up following a path other than that of Ahl al-Sunnah. This will cause great hardship and difficulty to their mother who follows the way of Ahl al-Sunnah wa’l-Jamaa’ah.
In conclusion, according to the scholars of Ahl al-Sunnah it is strongly makrooh for a woman to marry a Muslim man who follows bid’ah, because of the bad consequences that will result from that, and because it will cancel out many good things.
And whoever gives up something for the sake of Allaah, Allaah will compensate him with something better than it.
And Allaah knows best.
See Mawqif Ahl al-Sunnah wa’l-Jamaa’ah min Ahl al-Ahwaa’ wa’l-Bida’ by Dr. Ibraaheem al-Raheeli, 1/373-388.