Jesus Christ Himself doesn't agree with your premise
Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven. Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works? And then will I profess unto them, I never knew you: depart from me, ye that work iniquity. from me, ye that work iniquity. (Matthew 7:21-23)
The Lord taught that some people who self-identify as Christian will be excluded from His kingdom. But He also taught something else that the LDS Church completely believes in:
And John answered and said, Master, we saw one casting out devils in thy name; and we forbad him, because he followeth not with us. And Jesus said unto him, Forbid him not: for he that is not against us is for us. (Luke 9:49-50)
Those two verses seem to identify a paradox. On the one hand, people who self-identify as Christian are excluded. On the other hand, people who self-identify as Christian are included.
What the LDS Church believes is that Jesus' Kingdom is divided into various glories.1 The highest glory is reserved for those who embrace the testimony of Christ fully and who receive covenants and ordinances via the full authority of Christ (D&C 76:50-70).
Others receive a lesser glory, depending on their choices and commitment to the fullness of the gospel of Jesus Christ (D&C 76:71-89).2
So, where does the LDS Church draw the official line? Let's look at Alma 5:60:
And now I say unto you that the good shepherd doth call after you; and if you will hearken unto his voice he will bring you into his fold, and ye are his sheep; and he commandeth you that ye suffer no ravenous wolf to enter among you, that ye may not be destroyed.
So the line is drawn at people who would destroy the Church. Whether they self-identify as Christian or not. This sets the limit for exclusivity — but what about inclusivity? Let's look at D&C 46:3-5:
Nevertheless ye are commanded never to cast any one out from your public meetings, which are held before the world. Ye are also commanded not to cast any one who belongeth to the church out of your sacrament meetings; nevertheless, if any have trespassed, let him not partake until he makes reconciliation. And again I say unto you, ye shall not cast any out of your sacrament meetings who are earnestly seeking the kingdom—I speak this concerning those who are not of the church.
We are commanded of the Lord to not exclude anyone from our public meetings. This reflects Luke 9:50.
But what did you actually mean?
Unfortunately, your question is unclear. What do you mean by "reject" and "disallow?" There's a difference between how individual members of the Church act and what the Church teaches, depending on what you actually mean by those words.
It is an unfortunate and painful truth that individual members can and do act with introversion and exclusion. This is not the gospel of Jesus Christ, but like the ancient Jews of old, being told that:
- Yours is the "only true church of Jesus Christ."
- You are the "elect of God."
- You are the "chosen people."
can go to your head. It is a sign of apostasy to exclude others when the goal is to embrace them in love and offer them (whether they choose to accept it or not) every blessing the Lord has to offer. It is a constant struggle to help members avoid this particular sin.
But if what you meant by your question was something along the lines of what @DJClayworth mentioned, that "accept" and "allow" means to consider the authority, gospel, and opportunities offered by another church as equal to our own. The answer is no. We believe that no other church offers the fullness of the gospel of Jesus Christ, the fullness of the authority of the Melchizedek Priesthood, and therefore has not the authority to open the door to Christ's exaltation.
We accept all who are not against us as Christians, but we recognize (as the Lord taught) that not all will embrace the highest glory He has offered in His kingdom. And that includes our own membership.
1 Detailed explanations of the Degrees of Glory have been given elsewhere on this Stack. Rather than clutter this question with yet another detailed explanation, I'll summarize and otherwise defer to them.
2 I'm not summarizing Outer Darkness or Perdition here. It's a kingdom without glory, though still within the judgement and therefore kingdom of Christ. But it's not relevant to the discussion concerning those who self-identify as Christian unless they also happen to be someone entirely against Christ in all forms and in all ways. Bit of an oxymoron, there, but I guess it could occur.