Thank you very much for your suggestions. I'm going to take a close look onto your ideas.
But first I have to give you my recent observation: As you can see in my logs, I logged every time onto the Pfsense-Server. I logged by klicking on the CP-Login-Page 192.168.123.1:8000 (using a SSH-tunnel to the Server). It resulted in a login in the auth.log. As you see, I was thrown out within 60 Sec. This was also mentioned in the log. Today I used the local computers.
Result:
Oct 28 08:00:02 pfsense logportalauth[723]: LOGIN: gd, 02:0f:b5:c8:2f:1f, 192.168.123.106
Oct 28 08:32:01 pfsense logportalauth[55266]: TIMEOUT: gd, 02:0f:b5:c8:2f:1f, 192.168.123.106
Oct 28 08:54:31 pfsense logportalauth[723]: Voucher login good for 269240 min.: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 10:08:49 pfsense logportalauth[68280]: xyxyxy invalid: TYPO illegal character (U) found in 4U2RG8 !!
Oct 28 10:08:49 pfsense logportalauth[68280]: FAILURE: xyxyxy, 5c:8d:4e:3b:c3:9d, 192.168.123.173
Oct 28 10:09:18 pfsense logportalauth[68280]: Voucher login good for 269165 min.: xyxyxy, 5c:8d:4e:3b:c3:9d, 192.168.123.173
Oct 28 10:20:36 pfsense logportalauth[7555]: Reconfiguring captive portal(Seminar).
Oct 28 10:21:37 pfsense logportalauth[91985]: TIMEOUT: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 10:54:43 pfsense logportalauth[81922]: TIMEOUT: xyxyxy, 5c:8d:4e:3b:c3:9d, 192.168.123.173
Oct 28 11:19:44 pfsense logportalauth[23891]: Voucher login good for 269094 min.: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 11:19:59 pfsense logportalauth[23891]: CONCURRENT LOGIN - REUSING OLD SESSION: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 11:19:59 pfsense logportalauth[23891]: Voucher login good for 269094 min.: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 12:04:56 pfsense logportalauth[80944]: TIMEOUT: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 12:37:36 pfsense logportalauth[97699]: Voucher login good for 269017 min.: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 13:23:11 pfsense logportalauth[43792]: TIMEOUT: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 13:28:47 pfsense logportalauth[43520]: Reconfiguring captive portal(Seminar).
Oct 28 14:12:04 pfsense logportalauth[43039]: Voucher login good for 268922 min.: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 14:13:46 pfsense logportalauth[43039]: Voucher login good for 268920 min.: xyxyxy, 5c:8d:4e:3b:c3:9d, 192.168.123.173
Oct 28 15:05:51 pfsense logportalauth[43039]: DISCONNECT: xyxyxy, 84:a6:c8:38:26:ba, 192.168.123.147
Oct 28 15:34:11 pfsense logportalauth[27574]: TIMEOUT: xyxyxy, 5c:8d:4e:3b:c3:9d, 192.168.123.173
Oct 28 15:34:44 pfsense logportalauth[43301]: LOGIN: gd, f0:de:f1:be:6f:f1, 192.168.123.108
Oct 28 16:24:20 pfsense logportalauth[44795]: TIMEOUT: gd, f0:de:f1:be:6f:f1, 192.168.123.108
Unbelievable, isn't it? It seems to work! Everywhere - except on the Pf-machine! Well, I searched the responsible inc-File to learn, why it is so. But this is goint to take longer. In the moment I'm just happy, that it works (and possibly worked before).
Michael