All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
The cross is something that is worshipped instead of the worship of Allah, and the Sharee'ah established that it must be removed and that it should be obliterated, but not to spread and propagate it.
'Aa’ishah narrated that the Prophet never used to leave in his house anything containing images of the cross except that he destroyed and disfigured it. [Al-Bukhaari] "disfigured it" means, changing its look so that it does not look like a cross.
Ibn Hajar said: “This is because the cross is something that used to be worshipped besides Allah.” [End of quote]
Also, Imaam Ahmad in his Musnad, and An-Nasaa’i in As-Sunnan Al-Kubra reported that ‘Aa’ishah, may Allaah be pleased with him, was circumambulating the Ka’bah and she saw a woman with a kind of dress on which there was a cross, so the Mother of the Believers said to her: “Throw it away, throw it away; when the Prophet used to see something like this, he would destroy it.”
The scholars stated that it is not permissible to make/use the cross; the Fiqh Encyclopedia reads:
“It is not permissible for a Muslim to make a cross, and it is not permissible for him to order it to be manufactured. […] He is also not permitted to keep it, whether or not he wore it. It is also not permissible for him to display this slogan in the roads or streets of the Muslims, and their private or public places. Moreover, he is not permitted to stitch it onto his clothes, as ‘Udayy ibn Haatim narrated:
“I came to the Prophet while I was wearing a golden cross on my neck (as a necklace), so he said to me: “O 'Udayy! Throw away this idol.”
Additionally, Abu Umaamah narrated that the Prophet said: “Allah has sent me as a mercy and guidance to all mankind, and He ordered me to destroy the flutes, musical instruments, idols, the cross, and the matters of the Jaahililyyah (Pre-Islamic Era of Ignorance).” [End of quote]
The Fatwa of the Standing Committee reads:
“It is not permissible to take pictures of the cross or other symbols of disbelief, and then publish them in magazines and advertisements.” [End of quote]
As regards the question whether or not the one who uses the cross as a logo for him on social media becomes a disbeliever, then the answer is that if he uses the cross as a way of glorifying it while he knows that it is a slogan for Kufr (disbelief), then the answer is that it is likely that he becomes a disbeliever – we seek refuge in Allah from that.
The jurists stated that whoever glorifies the cross goes out of the fold of Islam. Ibn Al-Muflih, from the Hanbali School of jurisprudence, said in Al-Furoo’:
“If it was testified against someone that he glorified the cross, such as kissing it, and does the actions of the people of disbelief, and he often goes to the places of their worship, then it is probable that this is apostasy because such acts are done out of belief. However, it is also probable that he did not do so out of belief, because he may do so as a way of being kind to them [non-Muslims], or out of fear in order to gain a worldly benefit. However, the first view is the most preponderant one.” [End of quote]
Allah knows best.