Step or not. They can be a positive influence in their life but to tack "Mother" onto their title isn't appropriate.
I disagree entirely. Ex and I split when DS1 was 5 months old. I met now DH when DS1 was young and he's always called him by his name. Then DS2 arrived and within a year or so, DS1 had begun switching between "Dad" and "name". I explained to Ex that DS1 wasn't doing it to hurt anyone, that DH and I hadn't ever encouraged it, and that we'd let it go, knowing that DS1 knows who his Dad is. We're now many years on and DS1 calls them both Dad. It doesn't devalue his love or bond with Ex, and fortunately Ex was never concerned with anything but DS1's happiness, and was always thankful that DH was able to be "Dad" when he wasn't there.
I know it's become common to call Father's new wives StepMother but they're not a Mother to that child.
And now that Ex has married his DW, DS1 has a woman who loves him, cares for him, nurtures him when I'm not there. On Mothers Day for the past 7 years he's chosen her a card and gift with me, this year he said to me "she's my Mum when I'm not with you" and instead of hating her or feeling put out, I am eternally grateful that Ex has found a woman who cherishes my firstborn. There's no question over who DS1's parents are; it's all four of us. We've all loved him. We've all had to give him rollockings. We've all wiped his head when he has a migraine. We've all celebrated his successes and I'd like to think we'll all be there the day he marries, the day he graduates, the day he becomes a Father, celebrating brithdays, christmases and everything in-between.
There's more than one way to raise a child. There's more than one way to be a Mother. DS1's Step-Mother deserves her title, deserves my respect and deserves honouring just as any other Mother does.