No idea what to change.

I suggest you read
https://stackoverflow.com/questions/40724046/mysql-gtid-consistency-violation and
https://dev.mysql.com/doc/refman/5.6/en/replication-options-gtids.html

Maybe install without demo content

@ramadama Can you please try to change ENGINE = myisam to ENGINE = innodb for the table T_syslog on the line https://github.com/b2evolution/b2evolution/blob/7.0dev/inc/_core/model/__core.install.php#L702 of your local copy and then reinstall it on your server where you had the error "GTID consistency"? Thanks.

Thanks a lot Yura. I did as you suggested. Did not work much better.
Then i tried to install version 6.11.0 in same environment. Didn't work neither.

Set up a new database, this time using MySql 5.5 instead of 5.7.: worked with install of both b2e-versions!

I would say MySql 5.7. is causing the problem in this case.

Thanks a lot Yura. I did as you suggested. Did not work much better.

We can hardly make any progress if you give vague feedback like "Did not work much better.". We would need to see the exact difference between the previous error and the new error message.

The problem is likely due to a specific setup of MySQL 5.7 @ 1&1 and cannot be reproduced with a standard MySQL 5.7 install. Exact error messages are very important if you want us to be able to fix the issue(s).

You're right, not too many details. The installation with MySQL 5.7. db ended with the error message as in above screenshot.

And i have to say that i did not notice a difference between ENGINE = myisam versus ENGINE = innodb, as Yura suggested. If it helps I could do both options again and carefully document failure messages.

Despite the error message (and the not fully performed installation) with MySQL 5.7. db , i could sign in and when i added a new user, there was a similar failure/message as above documented. as this might hold additional information, i include it here.

The forth last line in the screenshot is longer than the screen shows, therefor i include this line as text line here:

sess_data = 'a:25:{s:22:\"crumb_latest_loginform\";a:2:{i:0;N;i:1;s:43:\"W1BTWRDTOjil9Rqb24rQ3Fol1Gm20ZFG-1555245349\";}s:11:\"core.pepper\";a:2:{i:0;i:1555331749;i:1;s:64:\"vY5lq8BpXhtT8NzLzLWcxglsLw3uHUZzPiKCGgr7qRGVodPBqWBkc3w8tcIC6PGO\";}s:22:\"crumb_latest_loginsalt\";a:2:{i:0;N;i:1;s:43:\"ZwivxtXGkuQZdugi86BiTmsx2t70Kg6p-1555245349\";}s:24:\"registration_trigger_url\";a:2:{i:0;N;i:1;s:60:\"http://dieklimaseite.de/b2e_test_70/admin.php?ctrl=dashboard\";}s:20:\"crumb_latest_regform\";a:2:{i:0;N;i:1;s:43:\"Rt1bOlXKLx0sBVfM9Y1zhby9XT6E5VHr-1555245354\";}s:15:\"wrong_loginpass\";a:2:{i:0;N;i:1;s:43:\"he:84211645e6c89fda70f5a4c4dc71f9c1e44081f5\";}s:25:\"crumb_latest_lostpassform\";a:2:{i:0;N;i:1;s:43:\"KAEXukUtg7zZMjNn8IIEfjP65B1odKKm-1555245481\";}s:24:\"core.no_CachePageContent\";a:2:{i:0;N;i:1;i:1;}s:18:\"collection_filters\";a:2:{i:0;N;i:1;a:0:{}}s:12:\"blog_filters\";a:2:{i:0;N;i:1;s:9:\"collapsed\";}s:17:\"crumb_latest_skin\";a:2:{i:0;N;i:1;s:43:\"9NvT2u7NU83Mtv8u0tVa4riBgSwehE0Y-1555675692\";}s:21:\"crumb_latest_siteskin\";a:2:{i:0;N;i:1;s:43:\"xxQ7XqqRtceCHwMgEDc3bfyoc64pOAyW-1555675692\";}s:23:\"crumb_latest_collection\";a:2:{i:0;N;i:1;s:43:\"zVYxJcSFPTG5AvrLliIem3a371cqspPT-1555247997\";}s:28:\"crumb_latest_file_attachment\";a:2:{i:0;N;i:1;s:43:\"esySTiZqZJwW7P4LDSLYBkRZC5hkVWZU-1555675688\";}s:17:\"crumb_latest_file\";a:2:{i:0;N;i:1;s:43:\"WG1PSZBlP7wFDYdd3cGFUFuNqd1PMKWH-1555248061\";}s:26:\"crumb_latest_conflictfiles\";a:2:{i:0;N;i:1;s:43:\"45mVlr1CbIMlvmwg4dzHs2b2S4SBKBAE-1555248061\";}s:18:\"crumb_latest_tools\";a:2:{i:0;N;i:1;s:43:\"AGi6KmrMlgeT38oY8eQ4yIdSRTDaOuFe-1555248201\";}s:19:\"crumb_latest_plugin\";a:2:{i:0;N;i:1;s:43:\"TeRZVUxOmyZRfaRG21I5oR1Km27I3iqB-1555248268\";}s:17:\"crumb_latest_user\";a:2:{i:0;N;i:1;s:43:\"PWadWg06ZJvlJUDIzP8Mcn77KvsjePZ5-1555248298\";}s:22:\"UserList_filters_admin\";a:2:{i:0;N;i:1;a:36:{s:13:\"filter_preset\";N;s:12:\"filter_query\";N;s:7:\"country\";N;s:6:\"region\";N;s:9:\"subregion\";N;s:4:\"city\";N;s:11:\"membersonly\";b:0;s:8:\"keywords\";N;s:6:\"gender\";N;s:16:\"status_activated\";N;s:14:\"account_status\";N;s:14:\"registered_min\";N;s:14:\"registered_max\";N;s:8:\"reported\";N;s:19:\"custom_sender_email\";N;s:18:\"custom_sender_name\";N;s:5:\"group\";i:-1;s:6:\"group2\";i:-1;s:7:\"age_min\";N;s:7:\"age_max\";N;s:5:\"order\";s:19:\"/user_lastseen_ts/D\";s:5:\"users\";a:1:{i:0;s:1:\"1\";}s:7:\"userids\";a:0:{}s:9:\"level_min\";N;s:9:\"level_max\";N;s:3:\"org\";N;s:10:\"newsletter\";N;s:14:\"not_newsletter\";N;s:21:\"newsletter_subscribed\";i:1;s:4:\"ecmp\";N;s:14:\"recipient_type\";N;s:16:\"recipient_action\";N;s:8:\"user_tag\";N;s:12:\"not_user_tag\";N;s:10:\"reg_ip_min\";N;s:10:\"reg_ip_max\";N;}}s:35:\"UserList_filters_admin_refresh_time\";a:2:{i:0;N;i:1;d:1555246800;}s:22:\"crumb_latest_userlevel\";a:2:{i:0;N;i:1;s:43:\"46WqLUU1xAyp3VyaMn4QoVDt7Z0MxFrD-1555248298\";}s:25:\"crumb_latest_usersettings\";a:2:{i:0;N;i:1;s:43:\"bleAURukzrGDRT5ssOla2UGf9hPjJk8t-1555248321\";}s:20:\"crumb_latest_userorg\";a:2:{i:0;N;i:1;s:43:\"st6HsXQRGwn8WrquYg54xgEinSSga1WD-1555248395\";}s:31:\"crumb_latest_collectionsettings\";a:2:{i:0;N;i:1;s:43:\"9LiNAtj74o4gKDzGM9Xkj0GQNmpQGUVJ-1555675688\";}}',

If I can or should produce additional documentation, you have to advise me what to do and i can try.

For my purpose the case is 'solved', as the installation is working well with MySQL 5.5. ...