> I can disable seeing their retweets but I can't disable seeing their likes.
You can stop seeing "likes" (in general, not from a specific person) if from the official client you mark the tweet as "I don't want to see this" (I don't know the exact message in English) and after giving this negative feedback several times about likes, the client stops showing them.
Use the "Latest Tweets" mode instead of Home, you can switch from the stars icon in the top right.
Latest tweets doesn't show likes for me, ever.
That, and also clicking "I don't like this" on a bunch of other algorithmic suggestion boxes, means I'm seeing just the regular old timeline of what people [re]tweeted...
