This coming Sunday's reading is John 6:37-40. In the reading, Jesus says, "I will not reject anyone who comes to me, because I came down from heaven not to do my own will but the will of the one who sent me".
So, then, if Jesus does not reject anyone who comes to Him, on what basis could we reject anyone who seeks Jesus? There is no basis.There is no category, no type of person, whom we have the power or authority to prevent from approaching Jesus. The Church itself tries to be the arbiter of who can come to Jesus, for instance in limitations on divorced persons receiving Communion, but the Gospel provides no basis for this.
The only thing that I can say in this regard is that if anyone thinks they are the arbiter of who should be allowed to go to Jesus, they had better be right. Jesus seemed always to want to be the last word on who could come to him.