They allow mixing in the mosque because they want people to attend
Question

                In our mosque , during ramadaan, around iftaar time, there is mixing between men and women. This has gone on for many years. The people who run the mosque use the excuse that if we do not let the people do what they want they won't come to the masjid. Also, during taraweeh they do many innovations, for example they do a tasbeeh after every four raka'aa. What advice can you give me to correct the situation?.
Praise be to Allah.
      Firstly: 

    Free mixing between men and women is haraam, because it leads 
    to many negative consequences and haraam things. We have quoted the evidence 
    for the prohibitions on mixing in the answer to question no. 
    1200. 

    As mixing is forbidden at all times and in all places, then 
    it is more emphatically forbidden if it is done in the mosques during the 
    month of Ramadaan, because it goes against the shar’i aims for which mosques 
    are established, such as maintaining and propagating Islam, calling people 
    to good and forbidding them to do corrupt and evil things. It also goes 
    against the reason for fasting, which is so that we might attain piety 
    (taqwa) and avoid whims and desires.  

    All the people of the mosque should denounce this evil and 
    strive to do away with it. Those who are in charge of the mosque are 
    especially responsible. 

    No one has the right to try to justify this evil or to remain 
    quiet about it on the grounds that not allowing mixing may cause some people 
    to refrain from coming to the mosque. This argument is to be rejected on 
    several fronts: 

    1 – Remaining quiet and not denouncing evil when one is able 
    to do so means that one is sinning. The Prophet  (peace and blessings of 
    Allaah be upon him) said: “Whoever among you sees an evil act, let him 
    change it with his hand (by taking action); if he cannot, then with his 
    tongue (by speaking out); and if he cannot, then with his heart (by at least 
    hating it and regarding it as evil) – but that is the weakest of faith.” 
    Narrated by Muslim, 48. 

    No wise person would accept for his attendance at the mosque 
    to be a cause of his falling into sin. 

    2 – The most important role that the mosque plays is calling 
    people to goodness and warning them against evil. Hence those who are in 
    charge of the mosque must explain to the people that mixing is haraam, and 
    stop them doing it. 

    3 – The idea that these people will never attend the mosque 
    is merely conjecture. Even if we assume that it does happen, the established 
    principle among the scholars is that warding off evil takes precedence over 
    achieving good. 

    4 – A special place for women to gather can be set up, 
    whether it is in a particular corner of the mosque or even outside in a tent 
    or some such, and useful programs can be offered to them, which should be 
    supervised by women. 

    5 – The daa’iyah is the one who should affect how things are 
    and strive to set things right; he should not be affected by things and then 
    look for justification. 

    Mixing is a problem that has arisen because we are far away 
    from Islam. Efforts must be made to denounce it and put an end to it. If the 
    first step is not taken in the houses of Allaah, then where shall we begin?! 
     

    You can work with some of your brothers to convince the 
    people in charge and help them to prepare a place that is suitable for women 
    to meet, and help them to prepare suitable programs for the women. 

    We ask Allaah to bless your efforts with success. 

    Secondly: 

    With regard to what you say about tasbeeh after each four 
    rak’ahs of Taraweeh prayer, we have stated in the answer to question no. 
    50718 that this is an innovation which should not be done. 

    Shaykh Ibn Baaz (may Allaah have mercy on him) was asked: 
    What is the ruling on raising our voices in sending blessings upon the 
    Prophet  (peace and blessings of Allaah be upon him) and praying that 
    Allaah be pleased with the Rightly-Guided Caliphs between the rak’ahs of 
    Taraweeh? 

    He replied: 

    There is no basis for that – as far as we know – in 
    sharee’ah, rather it is an innovation and should not be done. The affairs of 
    the later generations of this ummah will never corrected except by that by 
    which the affairs of the earlier generations were corrected, which is 
    following the Qur’aan and Sunnah and the way of the earliest generations of 
    this ummah (the salaf), and avoiding whatever goes against that. End quote. 

    Majmoo’ Fataawa Ibn Baaz, 
    11/369. 

    And Allaah knows best.