Should I be worried about my boyfriend liking nude photos of girls through his priv twitter?

Ok so he always says that he wouldn't cheat on me, but several times he's done something stupid. The first time I know of was he asked a girl on tinder to send him nudes "as a joke" and then proceeded to add her on snapchat so i dont know what went on from there (he used to let me go on his tinder), the second time I know of was of a girl that he used to be friends with during his previous relationship and when that ended they got quite close. Then he met me and stopped speaking to her for about a year, but he messaged her how he missed their conversations and she'd deleted their conversations so asked what they used to talk about and then he sent her screenshots of them sharing flirty messages and nudes she had sent him, and then he said he was glad he got them (the nudes) she didn't respond to that. The third time I know of was the private twotter acc one that i do follow, but obviously i dont follow all the people he follows. There is a girl that we both follow (extremely pretty) and he likes her photos when she takes provocative photos which puts me down obviously. But then recently my friend who is also his friend asked if i knew he was liking photos of a girl in her underwear on his priv (i dont follow her so i couldnt see) so i had a quick snoop to see for myself on his phone and it turned out true. So now i dont know what to do. He doesn't like me being on his phone without him being there, and always says it's disrespectful to our relationship, and i admit to that but i just can't trust him. He knows how i feel about all of this stuff and liking selfies of pretty girls that he barely knows. He tells me when he thinks a girls photo is attractive and girls in public and it makes me feel so shit and he knows this. One time i unliked a popular girls instagram photo (she looks like cara delevigne and he's into that) and then he re-liked it when i gave him his phone back. If i ask him to not like certain girls photos he'll just ignore me and do it anyway.
Should I be worried about my boyfriend liking nude photos of girls through his priv twitter?
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