Can I remove myself from a group text?

Yes, only if your are on a Group iMessage and not if you are on Group SMS or Group MMS

Add or remove someone from a group conversation

Anyone in a group iMessage can add or remove someone from the conversation. You can remove a person from a group iMessage that has at least three other people. You can’t add or remove people from group MMS messages or group SMS messages.

Types of group messages

The three types of group messages that you might see are: group iMessage, group MMS, and group SMS. The Messages app automatically chooses the type of group message to send based on you and your recipients' settings, network connection, and carrier plan. For example:

• If you and your recipients are using Apple devices and iMessage is turned on, then the group message is sent as an iMessage.
• If you send a group message to people who aren't using iMessage, then the message is sent as an MMS or SMS message. All responses in a group SMS are sent as individual text messages and the recipients can’t see the other responses from the group.

If --> Can't mute group messages - Messages Help - Google Support

la4905 Said:

"Can I remove myself from a group text?: I am in a group text with sooke and android users. I want out! How???"

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Exiting a Chat Session:

Of you are note the Moderator, then you cannot be removed. Your only option is to backup your iPhone to a computer, and then restore it from this backup.