I personally didn't mean any offence to anyone who has ME, or any long term medical condition. I didn't read anyone else's posts that way either, though obviously can't speak for them.
Listen, the OP's circumstances are already tough. Lone parent. Full on job. I'm in that place too. Starting a new relationship means giving as much thought to the practicalities as to the feelings involved. At least, it has done for me.
My DH was being treated for cancer for a year before he died. It's a very different illness, of course, but having lived through that once - absolutely willingly for the man I loved - and seen the effect on my kids, I couldn't walk into a new relationship where I thought there was a high likelihood of further caring responsibilities. And from what she explains of this chap - that he's so affected by his ME that even while single with no kids he isn't well enough to work, sounds to me like the hurly burly of family life would be a lot for him, and impact on his health further, and lead to those caring responsibilities.
So I was very much coming from that perspective to the OP. That it's not selfish of her to want to put her kids first.
I did say that if I were single and met someone in this chaos situation it wouldn't put me off. But with children it's different.
Again, no offence intended. I know from how my DH often felt that the fear of being a burden can be awful in long term conditions. But I was in love with him and married to him and I wouldn't for a moment have left him to go through all that on his own. It was awful, but we still loved each other through it and laughed and had fun, and his life had value until the very, very end.