To address your points:
Christians are compelled by Christ to be altruistic.
Christians are compelled by Christ to sacrifice in our daily lives
The Beatitudes outline the blessed nature of the weak
The chief purpose of man is to glorify God
I see quite a bit of conflict here.
Jesus stands at the door and knocks - he doesnt blow down the door. If you are seeing Christians being compelled in any sense, you are missing the gospel. We are not loved because we obey but we want to obey because we are loved. Altruism and sacrifice are worthless works if they are not freely given of a willing heart - and God alone can know that.
There is nothing intrinsically meritorious or good about weakness.
Nothing. The
only good of human weakness is that it makes us dependent upon God, who is completely without weakness. The weak are blessed
because they look to God for their strength instead of themselves.
The young lions lack and suffer hunger; But those who seek the Lord shall not lack any good thing
Non nobis Domine, non nobis, sed nomini tuo da gloriam. Yes, that is true but I would not expect a 'rationalist" philosophy to incorporate this.
If Objectivism is "the concept of man as a heroic being, with his own happiness as the moral purpose of his life, with productive achievement as his noblest activity, and reason as his only absolute." That conflicts only as our own happiness is not our
highest moral purpose (see non nobis above) and that our reason is not on an absolute throne above God himself. Indeed reason, like our emotions and our body, should be our servant, and not our master.
Again, as a rationalist philosophy who denies what may exist but cannot be seen, I dont think Objectivism is compatible with any religion per se but again, I consider it's value more for its economic considerations.
Think of it more as a Wesleyan injunction (make all you can and save all you can, so you can give all you can) for those who consider themselves "enlightened" above "mere" religious superstition.