First of all every Christian must follow their Spirit guided conscience in regard to this topic..
Would the Spirit give a directive that contradicts a very direct teaching from Jesus Himself?
So if you are convicted that you should not engage in public prayer then don't do it and if you are convicted that you should join in public prayer then do it..
It's not a matter of unfounded conviction. It is a direct command:
5 “And when you pray, do not be like the hypocrites, for they love to pray standing in the synagogues and on the street corners to be seen by others. Truly I tell you, they have received their reward in full. 6
But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you.
How can someone be 'convicted' and go against a direct teaching of Christ?
But as for the scripture on the topic.. We must take in ALL that is written on the subject, let me quote the passage and point out some critical words..
Matthew 6:5 - Matthew 6:6
(Matthew 6:5-6) "¶ And when thou prayest, thou shalt not be as the hypocrites are: for they love to pray standing in the synagogues and in the corners of the streets, that they may be seen of men. Verily I say unto you, They have their reward. {6} But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly."
Note in the above scriptures it is not only about how they are praying ( Public ) but WHY they are praying in public to be SEEN by other men..
Which is why I've asked over and over is it possible to pray in public to "NOT be seen by other men?"
I would also like to point out not only does Jesus say what you highlighted (they pray to be seen by men) , but He also tells us where and how to pray.:
But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret
Then He tells us why to pray this way:
and thy Father which seeth in secret shall reward thee openly."
So again, it's not just about our motivation for praying that is being discussed here. It's about following the directions Jesus Gives on when, where and why Jesus says pray this way.
Not only that, the directive He gives on prayer are also mirrored the other two works He requires of us mentioned in mat 6. In that we are to give in secrete, and to fast in secrete. Which make sense, in that whatever we do for God we do not do it publicly, but in secrete. So when we pray we go to our rooms and close the door so as to not even be seen by out family. When we give we are to do so to not be seen by others. When we Fast we do it in such a way as to not let others know we are fasting. So everything we do for God is to be done quietly.
The way you read this passage says we are to fast and give in secrete but it is ok to announce your prayers publicly, so long as you do so with good intentions...
If this is the case then could you not also fast and give publicly if you have 'good intentions?' If so then why did Jesus waste almost a whole chapter in the sermon on the mount telling us otherwise?