Some people said that you cant go to hajj with your step mother but how ? Your step mother is your mehram you cant do nikaah with her so why is it so then ?
First of all the wife of the father is a mahram and she is quoted among the first whom a man can't marry : Allah the almighty says:
And do not marry those [women] whom your fathers married, except what has already occurred. Indeed, it was an immorality and hateful [to Allah ] and was evil as a way. (4:22)
Therefore travelling with her or going with her to hajj or 'umrah is permissible unless there's a risk that you may fall in a sin like that of the linked post.
Yes you can proceed with step mother . Actually Islam bound to travel with a female whom you can legally marry. A women who is in Nikah with father can not legally marry with husband's son. It is also morally obligatory to us to respect her and treat her as we treat with our real mother
step mother is like real mother until she is in Nikah with our father and we can go with her to hajj. If she get divorce then you will not be able to go with her on hajj.
being stepmother sometimes occurs so much pressure because people like to have comparison between step mother and biological mother, from a ayah we can will have idea of respect ofstep mother that:
"your lord has decreed:do not worship any but him;
be good to your parents;and both or any of them attain old age with you ,do not say to them even fie neither chide them but speak to yhem with respect and humble and tender to them and say: "Lord show mercy to them as they nutured me when i was small"
and step mother is also mehram to us as ALLAH says;
"AND do not marry those whom your father married indeed it was imoral and hateful to ALLAH[surah nisa ayat 22]
so from all these eviddence we are allowed to go and perform hajj with step mother.