I've got a little bit of experience with this. If they can clearly argue they're in a different category to you, then unfortunately I don't think you have a case.
Having said that, can't do any harm to send them a professionally worded, scary letter. They might not know you don't have a case and may be scared enough to comply with your requests.
Is them doing that really harming your brand? There's a difference to causing possible confusion and harming your brand. Are you actually losing sales because of their products?
Likely I will use them as a case study to show how easily the general public are manipulated, and enjoy the compliment. Absolutely, if it's in a different class there's nothing I could do legally to force them to stop using it, I could probably have 'the vegan army' destroy their social media presence but negativity doesn't really help anyone tbh. The woman behind the brand will no doubt make some cash and that's fine, personally I couldn't live knowing that what I do is killing people (in her defence she's probably ignorant to this)- but let's be honest if I all was chasing was cash I wouldn't have kept this gig going - and it is making me cash now. (sorry Chris - you gave me 6 months)
So remember folks, baby cow growth fluid is for baby cows - real men don't need it... or as a friend of mine so eloquently just wrote ....
Ever want a man to do something? Tell him it will make him a 'real man.' That woman is shaming personified (she clearly does a lot of it), it's all the more pathetic so many men fall for WOMEN telling them what a 'real man' is. How would they know? They don't have a clue.
More to the point, can you imagine the collective outrage if a male public figure went on TV, or wrote an article, telling women how to be 'real women'? 'Hey, you, get back to the kitchen - that's what REAL women do!' Pathetic, cultural relativism which is only ever acceptable in one direction.