As SJuan96 already pointed out in the comments, the EU does not forbid direct democracy. But of course there are certain rules that have to be obeyed when being a member of the EU - as is the case for a membership in any group. Acting against these rules and staying in the group will pose a problem (although reality shows that breaking the rules will be tolerated to a certain extent if the rulebreakers are determined enough).

Since joining a group brings the burden of adhering to the rules of the group, yes, this may limit the things people can decide via direct democracy. But this is not EU-specific. Switzerland, being part of the WTO, also has to adhere to the rules of the WTO. A group actually makes little sense if any member is to be allowed to always act as it wants.

As SJuan96 already pointed out in the comments, the EU does not forbid direct democracy. But of course there are certain rules that have to be obeyed when being a member of the EU - as is the case for a membership in any group. Acting against these rules and staying in the group will pose a problem (although reality shows that breaking the rules will be tolerated to a certain extent if the rulebreakers are determined enough).

Since joining a group brings the burden of adhering to the rules of the group, yes, this may limit the things people can decide via direct democracy. But this is not EU-specific. Switzerland, being part of the World Tade Organisation, also has to adhere to the rules of the World Trade Organisation. A group actually makes little sense if any member is to be allowed to always act as it wants.