Not all baptistic people feel that this should be the case, but those that don't remain a small minority.
One of those in this beloved minority, whom I have a great deal of respect for, is John Piper. His sermon, How Important is Church Membership, which I've previously posted here, is an excellent summary of his own thoughts and feelings on the subject, thoroughly supported by scripture. This sermon also contains a summary of his own actions in attempting to right this wrong within his own congregation.
Few other baptistic theologians share his views.
I was therefore delighted and surprised when I recently started reading Infant Baptism and the Covenant of Grace, by Paul K. Jewett, a Baptist. Let me share a brief quote from the preface, on page 5 of this book:
Though the traditional Baptist usage of closed communion, first challenged so eloquently by Robert Hall, has given way in our day to the more ultimate demands of Christian charity and unity, the practice of closed membership is still widely insisted on in Baptist circles. This, to me, is very unfortunate; for though the defense of infant baptism may not be a good cause, it does not follow that the people who make this defense are not good Christians and worthy members of the Christian church. To have the conviction that baptism should not be administered to infants is quite different from the intolerance that excludes all dissent from the fellowship of the church. Polemical theology that would serve a good purpose must be irenic, not divisive.
Small baptistic sprinklings of charity such as this are enough to encourage me to not lose heart, entirely.