Mark 15:21 And they compel one Simon a Cyrenian, who passed by, coming out of the country, the father of Alexander and Rufus, to bear his cross.
Using Strong’s Concordance:
Cross 4716. σταυρός stauros; from the base of 2476; a stake or post (as set upright), i.e. (specifically) a pole or cross (as an instrument of capital punishment); figuratively, exposure to death, i.e. self-denial; by implication, the atonement of Christ:
Translated in the King James Version – ‘cross’ 28 times
Whether the ‘stauros’ had a cross-piece forming a ‘T’ or a ‘Cross’ cannot be determined from scripture.
There is nothing in the New Testament which would encourage the wearing of a cross or the placing of a ‘cross’ outside a Church building.
I hope you find this helpful.