Your first mistake is assuming that a movement will always stay true to its intended purpose. It is not impossible for an ideology to become corrupted and loose its original values. Have you ever took a hard look at and scrutinized the actions and current beliefs of the people spreading and endorsing these ideologies? I myself believe in equality regardless of gender, race, sexual orientation, or creed. I see people as people. However after seeing the changes and increasing hippocratic nature of these movements I've no longer endorsed them and have begun to oppose them. By definition social justice does mean what you think it does but the dictionary definition is a far cry from the current movement that can be observed in the US and many western nations today. Just as feminism, a once righteous movement has fed into a warped version of what it used to be. Interseciontal feminism, now the mainstream facet of feminism in the US/UK/AU, arguably causes as much inequality as it fights.
You are also mistaken by assuming "ultraconservative people" are the only ones against the bloated and deluded movement that is social justice. While it is not easy to prove, more and more people seem to be accepting and discussing the problem of PC culture going too far. Just look at what people like Christina Hoff Summers and Milo Yiannopolous are doing and the response that they've revived, while it is a mixed one they do have a fair amount of support. Also it would seem like overbearing nature of PC culture is partly to blame for the support that a man like Trump has gained, as part of the reason why some find him appealing is that he challenges this ideology. Now I would like to reiterate that the people who are against Social Justice (which has lead to PC culture being what it is today) are not against equality nor solidarity, they are against the ridiculous things that it has brought about. In the UK you can be arrested for voicing a dissenting opinion against immigration on twitter (I'm not against the immigration but these measures are ridiculous), waving a flag bearing the cross of saint George has been banned in several towns in England as people are worried some might find it offensive, in canada a man was nearly brought to court simply due to the fact that he attempted to voice his dissenting opinion to a feminist activist on facebook, the list goes on and on and if you want more examples I will provide them.
My problem with feminism is that even inter-sectional feminism seems to ignore or laugh off male problems. Of which there are many. Men have a far higher suicide rate, homeless men are far less likely to find a service that will provide for them, DV shelters almost exclusively take in females despite the fact that in western countries approximately one third of DV victims are men, in the prison system women are handed lighter sentences for the same crimes for no reason other than being women, in family court cases men are far less likely to receive any form of custody than a woman, in the US women are twice as likely to get admitted into post secondary education and any STEM field, and as before the list goes on. My greatest issue with intersectional/modern feminism is that they regard MRMs as rape apologists (MRMs sometimes protest the guilty until proven innocent approach in rape cases) and attempt to discredit such movements without stopping to realize that men face their own set of problems (this can be observed by looking into articles puplished by VICE, BBC, and organizations like BuzzFeed/MTV). As far as the wage gap goes... I know this is lazy but I'll leave you a link here explaining why it is false http://www.washingtonexaminer.com/harvard-prof.-takes-down-gender-wage-gap-myth/article/2580405 if you want to discuss it further I suppose I could find the more hard information that I came across when listening to Milo and CHS.
Look, I have nothing against you and you seem to be supporting these movements with good intentions but I simply ask you to be skeptical of even the things that you believe in. If you wish to discuss this further we could perhaps exchange information so we wont have to use this comment section. Also note that I very much dislike the idea of being misinformed and while it might sound pretentious or silly I researched these issues intensely before giving up on the ideologies that I had believed in. Let me know what you think, if you are planning on another rebuttle perhaps we could take this conversation elsewhere.