Praise be to Allah.
Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him) was asked this question and he said
If this brother wants to pay your expenses for Hajj, so that going with him will not cost you anything, then it is OK for you to go on Hajj with him, but you do not have to go for Hajj with him. The reason why we say that it is not obligatory is because this brother is doing you a favour, and there is the fear that some day he may no longer be a brother in Islam to you [i.e., problems may arise between you and you may no longer be close], then he may remind you of his favour and say, “This is what I get for having taken you on Hajj with me in such-and-such a year, and now you have done this to me…!”
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